Question

prove that 2✓7 is irrational give that ✓7 is irrational​

Answer 1

Let 2√7 be a rational number.

Rational numbers can be expressed in the form p/q, where p and q are co-prime and q≠0

$2\sqrt{7} = \dfrac{p}{q}$

$\implies \sqrt{7} = \dfrac{p}{2q}$

p/2q is a rational number.

=> √7 is a rational number

But this contradicts to the fact that √7 is irrational

Hence, our assumption is wrong.

$\boxed{\boxed{\bold{Therefore, \ \sqrt{7} \ is \ an \ irrational \ number}}}}$.

                                                           

Answer 2

$\huge \mathtt{ \fbox{Solution :)}}$

Given ,

• √7 is an irrational number

Let , 2√7 is a rational number

Thus ,

➡2√7 = a/b

➡√7 = a/2b

Here , √7 is an irrational number but a/2b is an rational number

Since , irrational ≠ rational

Thus , our assumptions is wrong

Hence , 2√7 is an irrational number

_____________ Keep Smiling ☺