Question

Classify the following number as rational or irrational:
$\dfrac{{\sqrt {12} }}{{\sqrt {75} }}$
A. Rational
B. Irrational
C. Can’t be determined
D. None of these

Answer 1

Hint – In order to get the answer of this question we need to simplify the given numbers then we can choose the correct option according to the number obtained.

Complete step-by-step answer:
First of all you should know that If a number that can be expressed in the form of p/q is called rational numbers. Here p and q are integers, and q is not equal to 0. A rational number should have a numerator (p) and denominator (q). Examples: 10/2, 30/3, 100/5.
An irrational number is a number that cannot be expressed as a fraction for any integers and irrational numbers have decimal expansions that neither terminate nor become periodic. Example- \[\pi\].
The given number is $\dfrac{{\sqrt {12} }}{{\sqrt {75} }}$
We can also write $\dfrac{{\sqrt {12} }}{{\sqrt {75} }} = \sqrt {\dfrac{{12}}{{75}}} = \sqrt {\dfrac{4}{{25}}} = \dfrac{2}{5}$………….(Since the square root of 4 and 25 is 2 and 5 respectively)
 So, $\dfrac{2}{5}$ is a rational number.

Note – In this problem we have simplified the given term and got a number in the form of $\dfrac{p}{q}$ and any number which can be written in the form of $\dfrac{p}{q}$ where $q \ne 0$ is a rational number. Proceeding like this will give you the right answer.