Question

prove root 7 / root 6 is irrational​

Answer 1

6 + √7 is irrational number

Let us assume that, 6 + √7 is a rational number

=> 6 + √7 = a/b

Here, a and b are co-prime numbers.

=> √7 = a/b - 6

=> √7 = a - 6b/b

Here..

a - 6b/ b is rational number.

So, √7 is also a rational number.

But we know that √7 is irrational number.

So, our assumption is wrong.

6 + √7 is irrational number.