prove it!!!!!!!!!!!!!!!!!!!!(3)

Prove that $\sqrt{2}$ is irrational number

#Algebra #NumberTheory #AlgebraicManipulation #ProofTechniques #Proofs

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Let us assume √2 is a rational number Then it can expressed in the form of p/q where p and q are integers and q is not equal to 0 √2=p/q Cancelling common factors √2=a/b where a and b are co primes Squaring on both sides 2=a square/ b square 2/b square= a square. .... (1) 2 divides a square Therefore 2 divides a a=2c for some integer c Putting a = 2c in (1) We get 2b square = 4c square 2 divides b square 2 divides b Therefore a and b have at least 2 as their common factors Therefore a and b are not co prime So, this contradiction has arisen due to our wrong assumption √2 is irrational

Sanchet Katakol - 6 years, 8 months ago

Simply by long method of finding square root...we will find that the result is neither terminating nor repeating.

gunit Varshney - 6 years, 8 months ago

Really how so?

A Former Brilliant Member - 6 years, 8 months ago

what will be the value of 1

AMIT MAJUMDAR - 6 years, 8 months ago

What is 1 amit majumdar

Sanchet Katakol - 6 years, 8 months ago

Vaibhav Sharma - 6 years, 8 months ago

copied!!! at your own risk

Sanchet Katakol - 6 years, 8 months ago

Firstly we have to know the definition of rational number. If we can write a number in the form p/ q, where p& q are integer and q>0. Then we can assure that is an rational number . Otherwise it is an iretional number.

Tarek Aziz - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$