Question

Simplify $\sqrt {\dfrac{{10}}{{81}}} $?

Answer 1

Hint: Given a radical expression in fraction form. We have to evaluate the expression. First, we will write the expression as a quotient to radicals. Then, we will find the factors of the numerator and denominator in the expression. Then, we make pairs of the factors and move out the perfect square factors of the expression.

Complete step by step solution:
We are given the expression, $\sqrt {\dfrac{{10}}{{81}}} $. First, write the expression as a quotient of two radical expressions.
$ \Rightarrow \dfrac{{\sqrt {10} }}{{\sqrt {81} }}$
Write the factors of the numerator and denominator.
$ \Rightarrow \dfrac{{\sqrt {10} }}{{\sqrt {81} }} = \dfrac{{\sqrt {2 \times 5} }}{{\sqrt {9 \times 9} }}$
Now, move out the number which is the perfect square inside the radicand.
$ \Rightarrow \dfrac{{\sqrt {10} }}{9}$

Hence, the simplified form of the expression $\sqrt {\dfrac{{10}}{{81}}} $ is $\dfrac{{\sqrt {10} }}{9}$.

Additional Information:
The square root of a number is equal to the number itself when it is multiplied by itself. The number represented inside the square root symbol is known as radicand and the symbol is known as radical. The square root of the numbers is obtained by finding the perfect square of the radicand. The perfect square is denoted as a product of two equal numbers. Some numbers cannot be represented as perfect squares which means the square root of that number is not easy to obtain. The square root of such numbers can be obtained by the long division method. The radical expression as a quotient of two radicands can be written as $\sqrt {\dfrac{a}{b}} = \dfrac{{\sqrt a }}{{\sqrt b }}$

Note: Rational expression involving radicals can be represented as a quotient of radical expression. The numbers are represented as their prime factors. These factors tell whether the number is a perfect square or not.