Question

classify 5+5√5 is rational or irrational number​

Answer 1

We will prove this through contradiction.

So, Let us assume that 5+5√5 is rational.

Then,

5+5√5=

$\frac{a}{b}$

Where a and b are co primes.

$5 + 5 \sqrt{5} = \frac{a}{b}$

$5 \sqrt{5} = \frac{a - 5}{b}$

$\sqrt{5} = \frac{a - 5}{5b}$

Root 5 is irrational but we know that the other side is rational.

However this is not possible.

Hence, 5+5√5 is irrational.