Question

Prove that 3/√7 is an irrational number.​

Answer 1

Step-by-step explanation:

Let us assume to the contrary that 3/√7 is a rational number.

Therefore, 3/√7 = a/b ( Where 'a' and 'b' are co-prime and b≠0)

or 3b = a√7

or 3b/a = √7

Here, Rational number = Irrational number (since √7 is an irrational number)

This is not possible.

Therefore our assumption is contradicted.

This implies that 3/√7 is an irrational number.

Hence proved.

Answer 2

$\green{\underline\textbf{To find...}}$

✰✰ 3/√7 is an irrational number...

$\green{\underline\textbf{SoLution...}}$

Let 3 / √7 as an rational number...

So, it can be written in the form of a/b where a & b are co-prime numbers and integers...

3/√7 = a/b

3/√7 × a/b

3b = √7a

Hence, √7 is an irrational number...

So, our contradiction is wrong...

Therefore, 3/√7 is a irrational Number...