Question

How do you simplify $- \sqrt {\dfrac{4}{{25}}}$ ?

Answer 1

A square of a number is a number obtained by multiplying a given number with itself. The number whose square we found is called the square root of the obtained number. In this question, we are given a fraction whose square root we have to find.

That is we have to find the number whose square is equal to $\dfrac{4}{{25}}$ . So for that, we write the numerator and the denominator as a product of its prime factors and then see them individually if they can be written as a square of any number.

Thus, after writing the given fraction as a square of a number, we can find out its square root.

Complete step by step answer:
On the factorization of 4 and 25, we get –
$4 = 2 \times 2 = {2^2} \\\ 25 = 5 \times 5 = {5^2} \\\$
$\Rightarrow - \sqrt {\dfrac{4}{{25}}} = - \sqrt {\dfrac{{2 \times 2}}{{5 \times 5}}} = - \dfrac{2}{5}$

Hence, the simplified form of $- \sqrt {\dfrac{4}{{25}}}$ is $- \dfrac{2}{5}$ .

Note: The question is given in fraction form which has two parts, the upper part called the numerator and the lower part called the denominator, they both are separated by a horizontal line.

For simplifying a fraction, we have to write the numerator and the denominator of a fraction as a product of its prime factors and then divide both the numerator and the denominator by their common factor.

But in the fraction obtained after square rooting the given fraction, the numerator and the denominator are already prime factors so the given fraction is already simplified and thus cannot be simplified further.