Question

Classify the following numbers as rational or irrational with justification:

√12/√75
​

Answer 1

The number is a RATIONAL NUMBERS.

We know that a rational number is a number which can be expressed in the form of p /q where p and q are integers and q is not equal to 0.

Now,

Given Number :-

$\frac{ \sqrt{12} }{ \sqrt{75} } \\ \\ \\ \\ = \frac{ \sqrt{4 \times 3} }{ \sqrt{25 \times 3} } \\ \\ \\ \\ = \frac{2 \sqrt{3} }{5 \sqrt{3} } \\ \\ \\ \\ = \frac{2}{5}$

We know that :-

In 2/5, 2 and 5 are integers and 5≠0

Also,it is expressed as p/q form.

Thus,

It is a rational number.

This implies :-

Root12/Root75 is a rational number.