Question

S.T 3+2 root 7 is irrational whare 7 is irrational

Answer 1

Correct Question :

3+2√7 is irrational number, where √7 is irrational number.

To Prove :

3+2√7 is irrational number.

Solution :

Let assume 3+2√7 is rational number.

So,

$\implies\tt3 + 2 \sqrt{7} = \frac{ a}{ b} \: \: \: where \: a \: and \: b \:co \: prime\: no.\: and \: HCF(a,b) = 1.$

$\tt\implies 2 \sqrt{7} = \frac{a}{b} - 3. \\ \implies\tt2 \sqrt{7} = \frac{a - 3b}{b} \\ \tt\implies\sqrt{7} = \frac{a - 3b}{2b}$

Here, √7 is irrational number given above, but a-3b/2b is rational number.

$\tt Irrational \:\cancel{=} \: Rational.$

Our assumption is wrong.

Therefore, 3+2√7 is Irrational number.

Answer 2

Here is your answer user.