Question

give me correct answer of this question plzz....​

Answer 1

Step-by-step explanation:

Let us suppose square root of 3 is rational number and gcd of p and q is one.

Then it will be written as

$\sqrt{3 } = \frac{p}{q} \: \: (p \: q) = 1$

Squarring both sides

$3 = \frac{ {p}^{2} }{ {q}^{2} }$

${p}^{2} = 3 {q}^{2}$

Above equation shows p divides 3q and it must be of the form say

P=3K

Put P=3k in above equation we will get

$9 {k}^{2} = 3 {q}^{2}$

Solving further

We qet

${q}^{2} = 3 {k}^{2}$

Above equation show q is also a multiple of 3 means divisible by 3.

Its a contradiction because we have supposed the gcd of p and q is 1 means there are no divisors of p and q but we are getting divisors here. So square root of 3 is a irrational number.