Question

How do you find a square root of a fraction?

Answer 1

Hint: It is a descriptive form of an answer. Here in this question, we have to write the detailed explanation of the square root of a fraction. The rule where the square root of a fraction is involved is explained and also, we solve this question by considering the examples of square roots of a fraction.

Complete step-by-step solution:
 A fraction is a number which comes under the rational number. the rational number is represented in the form of \[\dfrac{p}{q}\]. In a fraction, there are three kinds namely, proper fraction, improper fraction and mixed fraction.
In generally the fraction is defined or represented as \[\dfrac{a}{b}\] where \[b \ne 0\]
when the square root is applied to the fraction, we have \[\sqrt {\dfrac{a}{b}} \]. The square root is also implied to both numerator and denominator also. so, it can be written as \[\sqrt {\dfrac{a}{b}} = \dfrac{{\sqrt a }}{{\sqrt b }}\]. this is applied to the both proper fraction and the improper fraction. if the fraction is a mixed fraction, then the mixed fraction is converted to the improper fraction and the same procedure is followed.
If the value of “a” and “b” are the perfect squares then the square root symbol will vanish; we obtain the solution in the form of fraction or in the form of whole number.
Let us consider one example. \[\sqrt {\dfrac{4}{9}} \]
This can be written as
\[ \Rightarrow \sqrt {\dfrac{4}{9}} = \dfrac{{\sqrt 4 }}{{\sqrt 9 }}\]
since the numbers 4 and 9 both are perfect squares and hence we have
\[ \Rightarrow \sqrt {\dfrac{4}{9}} = \dfrac{2}{3}\]
This is the way hoe we find the square root of a fraction

Note: When we want to find the square root of some number, let it be x. If x is a perfect square then we can obtain the result directly. Otherwise if x is not a perfect square let we factorise the x and if it possible we write the number in the form of exponential and then we simplify the number.