Question

Is 3✓11 an irrational number
With detailed explanation

Answer 1

Let us assume 3√11 is an irrational number in the contrary.

Then,

3√11=a/b (b≠0),

where a and b are co-primes.

So, 3√11=a/b

Rearranging it,

√11=a/3b

Now, since 3, a and b are integers, a/3b is a rational number. Which means that √11 is also a rational number.

But this contradicts the fact that √11 is an irrational number.

This contradiction arrived because we assumed 3√11 as a rational number.

Therefore, we conclude that 3√11 is a rational number.

MARK ME AS THE BRAINLIEST PLEASE.