Question

Prove that
$\sqrt{3}$
is irrational​

Answer 1

ANSWER IS IN THE ATTACHMENT

I HOPE THIS WILL HELP YOU

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Answer 2

Answer:

Prove that √3 is an Irrational:

Let us assume that √3 is a Rational Number.

Then it can be written in the form of p/q.

where p & q are Co Primes and q not equal to "0"

=> √3 = p/q

=> (√3)² = (p/q)² (Squaring on both sides)

=> 3 = p²/q²

=> 3q² = p²..................[1]

• It means 3 divides p² and also 3 divides p because each factors should be apper two times for the square to exist.

So we have p = 3r [ let "r" must be some Integer]

=> p² = (3r)² => p² = 9r² .............[2]

From equ [1] & [2]

=> 3q² = 9r²

=> q² = 3r²

where q² multiply of 3 and also q is Multiple of 3.

• So here p,q are common Multiples of 3 and they are Co Primes. Consequently p/q is not a Rational Number.
• So, √3 is an Irrational.

Step-by-step explanation:

Hope it helps you....

❣️Mr. Monarque❣️