Question

3root18 as rational or irrational

Answer 1

irrational number is the ans

Answer 2

3√18 = 3√(9×2)
= 3 × 3√2
= 9√2

9√2 is irrational.
Therefore, 3√18 is irrational.

Proof :
Let 9√2 be a rational number.
A rational number can be written in the form of p/q where p,q are integers and q ≠ 0

9√2 = p/q
√2 = p/9q

p,q are integers then p/9q is a rational number.
Then √2 must also be a rational number.
But this contradicts the fact that √2 is an irrational number.
So,our supposition is false.

Therefore, 9√2 is irrational number.