Alright, as Mr. UA-cam Math Man points out, these tricks only work if you are dealing with the same kinds of roots. Sqrt(2) * sqrt(75) As shown, we can combine these two numbers inside the same radical: = sqrt (2*75) = sqrt(150) Sadly, 150 is not a perfect square, but our work is not done yet. Notice that: 150 = 2*3*5*5 This means: Sqrt(150) = sqrt (2*3*5*5) = sqrt (6*25) = sqrt(25)*sqrt(6) When looking at a radical, think about it like a rescue mission. We are trying to “rescue” as much of a number as possible from being under the radical. We do this via prime factorization and the fact that if a or b > 0, sqrt(ab) = sqrt(a)*sqrt(b). So: Sqrt(25) * sqrt(6) = 5 * sqrt(6) = 5sqrt(6) So the answer is 5sqrt(6), which is probably about 12 if you asked an engineer.
I am an engineer and I would never say 5V6 is "about 12" which is a deviation of 100 . (12 - 12.25) / 12.25 = - 2.0 %... I would accept a deviation of -/+ 0.5% so I would say 12.23 < 5V6 < 12.27
Square roots show up in all kinds of real world math calculations, including carpentry, finance, statistics, sound, light, electricity, ... . Also, things like this often show up as a portion of what needs to be figured out in order to solve larger problems. It may not be as common as addition and multiplication, but it's common enough that it's important information to understand in order to be well rounded in Math.
I'm not sure if that's a serious question, but the point of this is not to discover what √2 × √75 equals. The point is to develop understanding and confidence in mathematics. The point of mathematics teaching is not to go through, one by one, every single exact calculation you will ever need to do in your life, so that you can rehearse them all with your teacher. That's a completely absurd expectation. Perhaps you meant to ask a different, less silly, question.
Alright, as Mr. UA-cam Math Man points out, these tricks only work if you are dealing with the same kinds of roots.
Sqrt(2) * sqrt(75)
As shown, we can combine these two numbers inside the same radical:
= sqrt (2*75) = sqrt(150)
Sadly, 150 is not a perfect square, but our work is not done yet. Notice that:
150 = 2*3*5*5
This means:
Sqrt(150) = sqrt (2*3*5*5) = sqrt (6*25) = sqrt(25)*sqrt(6)
When looking at a radical, think about it like a rescue mission. We are trying to “rescue” as much of a number as possible from being under the radical. We do this via prime factorization and the fact that if a or b > 0, sqrt(ab) = sqrt(a)*sqrt(b). So:
Sqrt(25) * sqrt(6) = 5 * sqrt(6) = 5sqrt(6)
So the answer is 5sqrt(6), which is probably about 12 if you asked an engineer.
I am an engineer and I would never say 5V6 is "about 12" which is a deviation of
100 . (12 - 12.25) / 12.25 = - 2.0 %...
I would accept a deviation of -/+ 0.5% so I would say 12.23 < 5V6 < 12.27
Also, Root(2)*Root(75) = Root(175) = Root(100*3/2)
= 10*Root(3/2) = 10*[Root(3) / Root(2)]
= 10*[ { Root(3) * Root(2) } / 2] = [10/2] * [Root(3*2)] = 5*Root(6)
got it sr of 75 = 5 X sr 3 then X sr 2 = 5 X sr 6 thanks for the fun
5 square root 6
Love those and your voice is calming.
Answer: 5 √6
-----------
√ 2 x √75
√2 x √5 x √5 x √3
5 x √2 x √3
5 √6
Thank you
5*6^1/2
sqrt(a)*sqrt(b) = sqrt(a*b)
V2 . V75 = V2 . 5V3 = 5V6
how about asking my iphone?🤣
√2 · √75 = √2 · 5 · √3 = 5√6.
Good job Mr. Math Man - you get 100+% and a big smiley face! And take off the rest of the day.
5 sq.root6
=5√6
Too easy
Sure it's easy ... *after* you learn how to do it and practice it a bit.
So give me a practical application where I’d wanna figure out what the square root of two times the square root of 75. Is.?
Square roots show up in all kinds of real world math calculations, including carpentry, finance, statistics, sound, light, electricity, ... . Also, things like this often show up as a portion of what needs to be figured out in order to solve larger problems. It may not be as common as addition and multiplication, but it's common enough that it's important information to understand in order to be well rounded in Math.
I'm not sure if that's a serious question, but the point of this is not to discover what √2 × √75 equals.
The point is to develop understanding and confidence in mathematics.
The point of mathematics teaching is not to go through, one by one, every single exact calculation you will ever need to do in your life, so that you can rehearse them all with your teacher. That's a completely absurd expectation.
Perhaps you meant to ask a different, less silly, question.