Question

Is the square root of 72 rational or irrational

Answer 1

72 = 2*2*2*3*3
     = (2*2)*(3*3)*2
so square root of 72 =2*3 *root 2
                                 = 6 * root2
since root2 is irrational therefore 6*root2 is also irrational 
Thus square root of 72 is not rational.

Answer 2

Given:

square root of 72.

To Find:

Is the square root of 72 rational or irrational.

Solution:

1) To find the square root of any number we will do it by the prime factorization and after it wee will find the square root by the pairing of the factors.

2) Rational numbers are the number which can be represented in the p/q form where p, q are integers and q can not be equal to 0.

3) While the irrational numbers are the numbers which can't be expressed in p/q form.

4) Prime factorization of 72

72 = 2 × 2 × 2 × 3 × 3

5) √72 = $\sqrt{2.2.2.3.3}$

on pairing we get

√72 = 2 × 3√2

√72 = 6√2

6) We all know that √2 is an irrational number and if we multiply any irrational number with any number than we get the irrational number only.

so √72 is an irrational number.