Wow….what about rational exponents? Does the order of application matter? Can’t 4^(2/3) power be written both ways, with the power inside or outside the radical?
In maths you often have variables to the power of and the minus sign is only included if it is in parenthesis or the variable is itself the negative number
In Excel, yes. Excel doesn't follow the standard order of operations, when it comes to "a minus ain't squared, unless it's been snared". Excel requires you to write -1*3^2 if you want it to evaluate as -9.
It's being used to illustrate a simple, yet common, mistake in handling exponents. The idea is to illustrate that point, rather than solve the problem.
If you are referring to -3^2 you can rewrite it as (-1)(3^2) which simplifies to (-1)(9) and then to -9 sense a negative sign can be treated as a -1 being multiplied by the original number(the 9 in this case) this property comes naturally
Someone who understands imaginary numbers would not make a mistake in the calculation on the RHS, but someone who does not understand the priority of calculations would not realize that the LHS is √-3²=√-(3×3)=√-9, √-3²≠√(-3)²=√9.
There’s something to do with principle roots making this inaccurate but I don’t remember what is is Edit: found it this has to do with functions and x which is kinda cheating as the real numbers and variables have different properties but incase anyone thinks they can do this to a graph I’ll correct them sqrt(x^2) is the same graph as |x| but converting the square root into a power we get x^(1/2)(2) which simplifies to x which is not the same as |x| so the property of converting n-roots into 1/n power doesn’t always apply
@@elreturner1227 how is it cheating when it is covered in exponentiation theorems and can be proven that (a^n)^m = a^(nm) so long you accept the definition that a+a+...+a = a^n
@@SEEANDPEA I’m hoping that you meant multiplication and not addition but even if it is multiplication that definition only works when n is a part of the set of all integers if you were to put 3/2 for n the definition you proposed falls apart because a*1/2a does not equal a^3/2
He probably meant multiplication. Kinda hard to type out these things on phones, and the * and + are right next to each other. The basis of laws of exponents start from the rule that a^n = a_1 * a_2 * … * a_n. Based from this rule, we can expand that (a^n)^m = (a_1 * a_2 * … * a_n)_1 * (a_1 * a_2 + … * a_n)_2 * … * (a_1 + a_2 * … * a_n)_m. Took me a long to type this out.
jakejacobs4411 writes: “-3 is a number. -3^2=9 not -9” No. There is a difference between -3² and (-3)². In the first case, the exponent only refers to 3. The result is then multiplied by -1. In the second case, the exponent refers to -3. Only if the minus sign and the base are in parantheses and the exponent 2 is outside the parantheses, you have a squaring of a negative number, otherwise not. That means: -3² = -1 ‧ 3 ‧ 3 = -1 ‧ 9 = -9 against (-3)² = -3 ‧ -3 = 9 Best regards Marcus 😎
@@GihanSankalpa-h1c writes: “how to i know if ^2 for (-3) or just for 3 ?” The crucial point are the parentheses. If, for example, you want to square -3, then the minus sign and the 3 must be in parentheses together and the exponent 2 must be outside the parentheses. Only then does the exponent 2 refer to -3 and not just to 3. That means (-3)² = 9. If, on the other hand, you have -3², then that is basically a shortened form of writing for -1 ‧ 3². Because in the order of mathematical operations exponentation always comes before multiplication, the exponent 2 only refers to the 3 and not to -3. It does not matter whether it is an implicit (-3²) or an explicit (-1 ‧ 3²) multiplication. In this case you have -3² = -1 ‧ 3 ‧ 3 = -1 ‧ 9 = -9 Best regards Marcus 😎
Thats correct only if the -3 is inside a bracket or parenthesis. (-3)sq. = 9 but -3sq. = -9 If the -3 is not inside bracket or parenthesis, then we first do 3sq. and the add the minus sign.
Sir , i have a question If: y=2^x Then why Y^2= 2^2x Why it is not Y^2= 2^x^2 Please mention my name in the title of the video . So that i can easily find the video
For example: if you have 2³ and you want to sqare this term, you have (2³)² = 2⁶ = 64 because 8 ‧ 8 = 64 and 2 ‧ 2 ‧ 2 ‧ 2 ‧ 2 ‧ 2 = 64 On the other hand 2^(3^(2)) is not equal to 64, but to 512. Because: 2^(3^(2)) = 2⁹ = 512 Best regards Marcus 😎
You absolutely CANNOT do what you did on the right hand side. Separation of square roots is ONLY ever allowed if at most one of the arguments are negative. For example: 2 = 1+1 = 1 +sqrt(1) = 1 + sqrt (-1*-1) [What you just did] Error comes here: = 1 + sqrt(-1)*sqrt(-1) = 1 +i^2 = 1-1 =0 Which is not equal to 2. So you cannot ever separate square roots if both arguments are negative.
What are you talking about? On the right side, the radical acts as a parentheses, so he could have written that as (sqrt[-3])^2, which undoubtedly is sqrt(-3)*sqrt(-3), as that is the very definition of what "squared" means. He didn't separate anything at all underneath the radical. Nothing of the sort. All he did was rewrite x^2 as x * x.
Go type "evaluate (sqrt(-3))^2" into google and see for yourself. The "separation" isn't a separation. Nothing was separated. He just re-wrote the squared term. x^2 = x * x. That's all he did. Then he factored out i^2 from the expression, which is also totally valid.
Hello everyone, without watching the video or reading other comments: √(-3²) = √(-1) ‧ √(3²) = i ‧ 3 = 3i against (√(-3))² = (√(-1) ‧ √(3))² = (i ‧ √(3))² = i² ‧ (√(3))² = -1 ‧ 3 = -3 Therefore the both terms are not equal. Best regards Marcus 😎
@@QuicksilverBL3DE the positive root is what's known as the "principal square root" and when you do operations, it's quite like you're doing functions: can't end up with more than one answer to the same question, just like in functions when it's said that one single input cannot result in two different outputs that's why we only count the positive root you may ask, why the positive root? couldn't mathematicians from back then make the principal root negative? sure, but the thing is that the mathematicians from back then thought of connecting mathematics with real life and so they got rid of the negative root
It is not the question, but you can also see that sqrt( (-3)² ) = sqrt(9) = 3 and ( sqrt(-3) )² = ( i*sqrt(3) )² = -3 so the order of "²" and "sqrt" is significant. If you only see "sqrt" as "power to 1/2" then you would expect that there is no distinction in the order and you could just cancel them out, but: sqrt( (-3)² ) ((-3)²)¹/² = (-3)²/² = -3
I mean you are being just purposefully confusing as many people will think of -3^2 as (-3)^2 The reason this is confusing has more to do with disadvantages of a notation system and less to do with understanding i
If it's not confusing to 7th graders, it's not confusing. This basic algebra concept is taught early on to middle school students. It's in every pre-algebra textbook I've seen.
@@mrhtutoring well if you had written it explicitly nobody would be confused and thus no reason for this video 😂. Not really sure what purpose of this was lol
@@arandomguy46 but in common language that is not how it's read. No point arguing with trolls. Grammer, including in mathematics, is not so rigid and there are ways to make points more clear. This is common knowledge and talked about consistently. Main channel is rage baiting
it's the normal rule like PEMDAS or so, exponentiation before multiplication. Just as someone else wrote before: You just have to be aware that -3² = (-1)*3² Then you see the order of operations...
@@BruceLee-io9by Not the way I and everyone else in my elementary school, high school. and university studied exponents. If there were parentheses denoting that this is -1 * (3^2) then yes but it is NOT denoted and therefore WRONG! I and every maths professor I've ever had would say the same thing.
@Thrakerzog In Italy it works like this: -3^2=-1*3^2 = -1*9=-9 while (-1*3) ^2= 9. If there is no parenthesis, -1 is not raised to the square, only 3 rises.
Summer study and its tips and tricks started right now...
Wow….what about rational exponents? Does the order of application matter? Can’t 4^(2/3) power be written both ways, with the power inside or outside the radical?
The exponent order is only interchangeable, if the base is positive.
Please write the title of the math problem you are trying to solve.
👍
Minus 3 squared is 9. You’ve done minus (3 squared) for some reason
I think you are correct. the first one is equal 3.
-3²=-9
(-3)²=9
-(3)²=-9
@@mrhtutoringdamn 🧐
√(-3²)=√(0-3²)=√(0-9)=√(-9)=3i
I would read the minus sign as part of the number that’s being squared. I’m not aware of any rule about this
Shouldn't there be parenthesis to make it clear?
No, the exponent rules are clear.
Following the rules, parentheses are not necessary.
In maths you often have variables to the power of and the minus sign is only included if it is in parenthesis or the variable is itself the negative number
@mrhtutoring Yes, that's true.
In Excel, yes. Excel doesn't follow the standard order of operations, when it comes to "a minus ain't squared, unless it's been snared". Excel requires you to write -1*3^2 if you want it to evaluate as -9.
Sir in √(-3^2) why can't we cancel our root from square ?
Won't the square of "-ve" become "+ve" because "-"×"-"="+"
Bad problem, they should never hinge on the interpretation of where an exponent goes
It's being used to illustrate a simple, yet common, mistake in handling exponents. The idea is to illustrate that point, rather than solve the problem.
Left side is objectively incorrect
-3^2 = -3*-3 = 9
Is this not correct?
Each other: -3
√ (-1 X 3) = j √3
(j√3)²= -1 X 3 = -3
No, 3i doesn’t equal -3
-3 squared is 9 not -9
Badly written
Sir i means
Even if we remove the square root at the beginning, they are also not equal.
It was multiply itself before the negative sign thats why the answer still negative
If you are referring to -3^2 you can rewrite it as (-1)(3^2) which simplifies to (-1)(9) and then to -9 sense a negative sign can be treated as a -1 being multiplied by the original number(the 9 in this case) this property comes naturally
I’m trying to answer the questions in comments but he’s already got to all of them
Awesome way of proving that.
Someone who understands imaginary numbers would not make a mistake in the calculation on the RHS, but someone who does not understand the priority of calculations would not realize that the LHS is √-3²=√-(3×3)=√-9, √-3²≠√(-3)²=√9.
wonderful
Wait.. Wb √-(x)² = |x|?? I love ur way of teaching, so asking ya.. I believe u'll help me get this out.
Can I ask question?
if we have same number inside radical when performing multiplication it should be multiply?
I should've had him in my 10th grade Algebra-He would have to coop his dad or Grandpa or get a DeLorean back to 1966.
Sometimes rewriting makes it easier to evaluate and know what to do by following exponential rules: (-3)^[(1/2)(2)]
There’s something to do with principle roots making this inaccurate but I don’t remember what is is
Edit: found it this has to do with functions and x which is kinda cheating as the real numbers and variables have different properties but incase anyone thinks they can do this to a graph I’ll correct them sqrt(x^2) is the same graph as |x| but converting the square root into a power we get x^(1/2)(2) which simplifies to x which is not the same as |x| so the property of converting n-roots into 1/n power doesn’t always apply
@@elreturner1227 how is it cheating when it is covered in exponentiation theorems and can be proven that (a^n)^m = a^(nm) so long you accept the definition that a+a+...+a = a^n
@@SEEANDPEA I’m hoping that you meant multiplication and not addition but even if it is multiplication that definition only works when n is a part of the set of all integers if you were to put 3/2 for n the definition you proposed falls apart because a*1/2a does not equal a^3/2
He probably meant multiplication. Kinda hard to type out these things on phones, and the * and + are right next to each other. The basis of laws of exponents start from the rule that a^n = a_1 * a_2 * … * a_n. Based from this rule, we can expand that (a^n)^m = (a_1 * a_2 * … * a_n)_1 * (a_1 * a_2 + … * a_n)_2 * … * (a_1 + a_2 * … * a_n)_m. Took me a long to type this out.
@@pensivenincompoop2016 oh that’s the wrong rule I mean transferring a square root to a fractional power
Absolut value of - 3 don't equal to - 3
-3² = 9 and not -9 right
I'm 100% certain that -3²=-9
@@mrhtutoring but how? We learnt in our school textbooks that the square of any number is always positive
The negative sign only applies to the 3.
If it's (-3)², then it's +9.
Root of - 3^ = + or - 3
And,
Root of - 3's^ = - 3.
Yes
Even after watching the video?
😂
3
-3 is a number. -3^2=9 not -9
jakejacobs4411 writes: “-3 is a number. -3^2=9 not -9”
No. There is a difference between -3² and (-3)². In the first case, the exponent only refers to 3. The result is then multiplied by -1. In the second case, the exponent refers to -3. Only if the minus sign and the base are in parantheses and the exponent 2 is outside the parantheses, you have a squaring of a negative number, otherwise not. That means:
-3² = -1 ‧ 3 ‧ 3 = -1 ‧ 9 = -9
against
(-3)² = -3 ‧ -3 = 9
Best regards
Marcus 😎
@@marcusgloder8755holy cow nobody told me about this.
@@marcusgloder8755 This was the only important point of the video, thanks.
@@marcusgloder8755how to i know if ^2 for (-3) or just for 3 ?
@@GihanSankalpa-h1c writes: “how to i know if ^2 for (-3) or just for 3 ?”
The crucial point are the parentheses. If, for example, you want to square -3, then the minus sign and the 3 must be in parentheses together and the exponent 2 must be outside the parentheses. Only then does the exponent 2 refer to -3 and not just to 3. That means (-3)² = 9. If, on the other hand, you have -3², then that is basically a shortened form of writing for -1 ‧ 3². Because in the order of mathematical operations exponentation always comes before multiplication, the exponent 2 only refers to the 3 and not to -3. It does not matter whether it is an implicit (-3²) or an explicit (-1 ‧ 3²) multiplication. In this case you have
-3² = -1 ‧ 3 ‧ 3 = -1 ‧ 9 = -9
Best regards
Marcus 😎
MARE BRÂNZĂ!
-3^2 = 9, how did he get root(-9) or did he just square the 3 like this -(3)^2?
-3²=-9
(-3)²=9
-(3)²=-9
@@mrhtutoring thank you
You have a strange opinion that -3 squared is -9 because only the 3 gets squared lol.
It's not my opinion.
It's a fact.
There’s no parentheses to give you (-3)^2=9. As it is written, you have -(3^2), which gives -9.
🤎
Shouldn't the square of -3 be 9 ?
He's Squaring ✓(-3). Not (-3)
Thats correct only if the -3 is inside a bracket or parenthesis.
(-3)sq. = 9 but -3sq. = -9
If the -3 is not inside bracket or parenthesis, then we first do 3sq. and the add the minus sign.
Sir , i have a question
If:
y=2^x
Then why
Y^2= 2^2x
Why it is not
Y^2= 2^x^2
Please mention my name in the title of the video . So that i can easily find the video
Exponential property
For example:
if you have 2³ and you want to sqare this term, you have
(2³)² = 2⁶ = 64
because
8 ‧ 8 = 64 and
2 ‧ 2 ‧ 2 ‧ 2 ‧ 2 ‧ 2 = 64
On the other hand 2^(3^(2)) is not equal to 64, but to 512. Because:
2^(3^(2)) =
2⁹ =
512
Best regards
Marcus 😎
Mr, on the left side of eq., it's squared on the 3 and not -3?
Square sign applies only to the 3.
it can only apply to -3 if it is inside the parenthesis. for example: “-3^2 = -9” and “(-3)^2 = 9”
You absolutely CANNOT do what you did on the right hand side. Separation of square roots is ONLY ever allowed if at most one of the arguments are negative.
For example:
2 = 1+1
= 1 +sqrt(1)
= 1 + sqrt (-1*-1) [What you just did]
Error comes here:
= 1 + sqrt(-1)*sqrt(-1)
= 1 +i^2
= 1-1
=0 Which is not equal to 2. So you cannot ever separate square roots if both arguments are negative.
What are you talking about? On the right side, the radical acts as a parentheses, so he could have written that as (sqrt[-3])^2, which undoubtedly is sqrt(-3)*sqrt(-3), as that is the very definition of what "squared" means. He didn't separate anything at all underneath the radical. Nothing of the sort. All he did was rewrite x^2 as x * x.
Go type "evaluate (sqrt(-3))^2" into google and see for yourself. The "separation" isn't a separation. Nothing was separated. He just re-wrote the squared term. x^2 = x * x. That's all he did. Then he factored out i^2 from the expression, which is also totally valid.
mrhtutoring you inspire me, i wish i was like you. I want to be a mathematician ❤ Plz reply
I wish you the best with your studies.
@@mrhtutoring I’m incredibly grateful for your reply. I can’t believe you took the time to answer me. Thank you sir
Hello everyone,
without watching the video or reading other comments:
√(-3²) =
√(-1) ‧ √(3²) =
i ‧ 3 =
3i
against
(√(-3))² =
(√(-1) ‧ √(3))² =
(i ‧ √(3))² =
i² ‧ (√(3))² =
-1 ‧ 3 =
-3
Therefore the both terms are not equal.
Best regards
Marcus 😎
What happened to the plus or minus after you finish from the square root?
Only the principal or the positive root is always used.
Only positive root is used when dealing with complex numbers?
@@QuicksilverBL3DE the positive root is what's known as the "principal square root" and when you do operations, it's quite like you're doing functions: can't end up with more than one answer to the same question, just like in functions when it's said that one single input cannot result in two different outputs
that's why we only count the positive root
you may ask, why the positive root? couldn't mathematicians from back then make the principal root negative? sure, but the thing is that the mathematicians from back then thought of connecting mathematics with real life and so they got rid of the negative root
You could just do this:
(√-3²)=(√-3)²
(√-3²)²=((√-3)²)²) the squared and square roots cancel
-3²=-3²
-9=-9 if you want to symplify then
-3=-3
((√-3)^2)^2) = (√-3)^4
-3^2=-3^2 is wrong
/-3² = /9 tho
(-3)²=+9
-3²=-9
You can always check it on mathway.com.
the negative isn't part of the base. We can expand -3^2 as -1*(3^2) and using GEMDAS or PEMDAS, we get -1*9 = -9.
@@mrhtutoring yeah sorry it was my fault
@@arandomguy46 thanks
No problem. 😀
It is not the question, but you can also see that
sqrt( (-3)² ) = sqrt(9) = 3
and
( sqrt(-3) )² = ( i*sqrt(3) )² = -3
so the order of "²" and "sqrt" is significant.
If you only see "sqrt" as "power to 1/2" then you would expect that there is no distinction in the order and you could just cancel them out,
but:
sqrt( (-3)² ) ((-3)²)¹/² = (-3)²/² = -3
I mean you are being just purposefully confusing as many people will think of -3^2 as (-3)^2
The reason this is confusing has more to do with disadvantages of a notation system and less to do with understanding i
If it's not confusing to 7th graders, it's not confusing.
This basic algebra concept is taught early on to middle school students.
It's in every pre-algebra textbook I've seen.
@@mrhtutoring well if you had written it explicitly nobody would be confused and thus no reason for this video 😂. Not really sure what purpose of this was lol
-3 can be thought of -1*3. It's not complicated.
@@arandomguy46 but in common language that is not how it's read. No point arguing with trolls. Grammer, including in mathematics, is not so rigid and there are ways to make points more clear. This is common knowledge and talked about consistently. Main channel is rage baiting
it's the normal rule like PEMDAS or so,
exponentiation before multiplication.
Just as someone else wrote before:
You just have to be aware that
-3² = (-1)*3²
Then you see the order of operations...
WRONG!!! -3 squared is ALWAYS +9
No need to yell.
-3²=-9 while (-3)²=+9.
You can always check it on online calculators such as mathway.com or wolframalpha.com.
Wrong, my friend. The teacher is right.
@@BruceLee-io9by Not the way I and everyone else in my elementary school, high school. and university studied exponents. If there were parentheses denoting that this is -1 * (3^2) then yes but it is NOT denoted and therefore WRONG! I and every maths professor I've ever had would say the same thing.
@Thrakerzog In Italy it works like this: -3^2=-1*3^2 = -1*9=-9 while (-1*3) ^2= 9. If there is no parenthesis, -1 is not raised to the square, only 3 rises.
@@Thrakerzog
A minus ain't squared, unless it's been snared.
WRONG. The square root of -3^2 is just 3
A minus ain't squared, unless it's been snared.
No. The square root of (-3)² is 3 but not of -3²