Question

How do you simplify: the square root of $ \dfrac{4}{9} $?

Answer 1

Hint: Here, we will find the square-root of the given fraction and then apply the property of square and square-root which cancels each other and will simplify accordingly for the required value.

Complete step-by-step answer:
Take the given expression: The square root of $ \dfrac{4}{9} $
Convert the given word statements, in the form of mathematical expressions-
The square root of
$ \dfrac{4}{9} = \sqrt {\dfrac{4}{9}} $
Square is the number multiplied itself and cube it the number multiplied thrice. Square is the product of same number twice such as $ {n^2} = n \times n $ for Example square of $ 2 $ is $ {2^2} = 2 \times 2 $ simplified form of squared number is
$ {2^2} = 2 \times 2 = 4 $ and square-root is denoted by $ \sqrt {{n^2}} = \sqrt {n \times n} $ For Example:
$ \sqrt {{2^2}} = \sqrt 4 = 2 $
Apply the concept of squares in the above expressions.
 $ \sqrt {\dfrac{4}{9}} = \sqrt {\dfrac{{{2^2}}}{{{3^2}}}} $
The above expression can be re-written as –
 $ \sqrt {\dfrac{4}{9}} = \sqrt {{{\left( {\dfrac{2}{3}} \right)}^2}} $
Square and square-root cancel each other in the above equation.
 $ \sqrt {\dfrac{4}{9}} = \dfrac{2}{3} $
This is the required solution.
So, the correct answer is “$\dfrac{2}{3} $”.

Note: Try to remember the squares and square-root of the numbers till at least twenty for an efficient and accurate result. In case the given number is big or you don’t know the squares you can find out using the prime factorization method finding the multiples for the given number.