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🔴 √2 is Irrational - Proof by Contradiction || Number Systems - 3 || in HINDI for Class 9 NCERT
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- Опубліковано 22 кві 2020
- In this Mathematics video in Hindi for class 9 we proved that square root of 2 is an irrational number using proof by contradiction. This is a topic from Chapter 1- 'Number System', Mathematics, Class 9, NCERT.
Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero.
We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.
From the equality √2 = a/b it follows that 2 = a²/b², or a² = 2 · b². So the square of a is an even number since it is two times something.
From this we know that a itself is also an even number. Why?
Because it can't be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd. Check it if you don't believe me!
Okay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don't need to know what k is; it won't matter. Soon comes the contradiction.
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2 = (2k)²/b²
2 = 4k²/b²
2*b² = 4k²
b² = 2k²
This means that b² is even, from which follows again that b itself is even. And that is a contradiction!!!
WHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.
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🔴 Click here to watch the whole playlist on Chapter 1 : 'Number Systems' for Class 9 :
• 🔴 Number Systems (Intr...
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Previous videos -
🔴 Number Systems (Introduction)
• 🔴 Number Systems (Intr...
🔴 Exercise 1.1 || Number Systems
• 🔴 Exercise 1.1 || Numb...
🔴 Irrational Numbers || Number Systems - 2
• 🔴 Irrational Numbers |...
You are a brilliant TEACHER.
Sir, why we not considered it as reducible in starting rather than irreducible..?
Irreducible means co primes
√2 = a/b where a and b are reducible so we reduce it and get p/q and therefore p and q do not contain any common factor other than 1 and therefore p and q are co-prime integers
Because if p/q is rational number then p,q must be co-prime numbers(according to rational number definition)
gcd of p and q is 1.( Acc to def. Of rational number)
We suppose √2 is rational
It implies √2= p/q and it is irreducible .
What an explanation sir ji, maza aa gaya👌
Thanks, sir you are awesome 🔥🔥😘😘
Sir what device do you use for writing?
If pc then you are a legend
Thank you sir
I am waiting for the video and l understand it ver easily
Sir, mujhe ye topic school walo or tuition walo ne yad karne ke liye kaha tha
Lekin apne ise samjhaya hain , thank you sir😊
😊😊😊😊🤗🤗🤗🤗😃😃😃😃👍👍👍👍
Koi bhi even 2k ke form me aata hai aur odd 2k+1 ke form me aata hai😁🙌gyan de rha hu😎
Thanks
Thank you sir 😇👍👍👍👍👍👍👍👍😇😇😃
Yes sir this vedio is really helpful and thanks for making this vedio
Sir bohot helpful video hain sir
Sir aap bohot dheri bolti hai
Lekin pura samagh mai agaya.
Jai hind
Hello sir , I have a doubt that ......
• At last we have proved that P and Q have a common factor of 2 .
•Means we can write (P as 2m and Q as 2q).
•So sir my doubt is that here , we can actually reduce (p/q) to the simplest form of fraction by cancelling 2 from both numerator and denominator. Such as for eg :- We can write (10/20) as (2×5 / 2×10) and can cancel 2 from both numerator and denominator to reduce it to the simplest form to make it coprime. ??
I have watched many videos related to this but have not understood it yet...
I will be really thankful to u if u can kindly clear my doubt.
Starting main hi bata diya tha ki dono 'p' and 'q' prime hain means Dono ka 1 hi factor hain
Isliye agar 2 factor aa raha aur vo aur reduce ho rahe hain iska matlab contradiction hua
@@sumitparmar6166 agar prime na ho to bhi to rational number hi hone 25/5 is rational even if 25 is not prime
Video is helpful for me sir thanx
sir very easy after i watch this video thank you so much sir
Thank you sir
ye mujhe samajh m aa he nhi raha tha
Thank you ❤
Thanks a lot sir
Best explanation about root 2 is irrational no..
U R GREAT SIR
U r the great sir 🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻
Thank you sir
Ur teaching is beautiful.
Thank you sir this helped me understand contradiction
Thanku sir I got it
Your teaching is slow
Thank you sir 🌷
Awesome ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
❤❤
Bak
Sir! √3 hoga to even kaise krege 2k???????????
Tab 2k nhi 3k hoga
@@Snow-w7otab vi nahi hoga .hoga to kaisa hoga?
THANKS, EASIEST EXPLANATION.
proof is clear
and thank u sir for making this video
U r g नी us
Sir ham√4 ko rational number he ye contradiction method se proof kar sakte hai kya
nhi shayad
kyuki , under root 4 gives us 2 and we can write 2 in the form of p/q i.e 2/1 . this proove hat root 4 is rational number .
q²=2k² kaise hogaya 4k² Kahan udd Gaya ?
10:25
(doubt)
Sir app bahut tough method se krwate ho
Didn't understood a thing
Sir with all due respect, you are purposely dragging your words.
Sq on number is not always even