Question

How do you simplify the square root \[\dfrac{{18}}{{32}}\]?

Answer 1

Hint: Here we have a fraction. They told us to simplify \[\sqrt {\dfrac{{18}}{{32}}} \]. We simplify the radicand that is the fraction to get the simplified from. We divide the numerator and denominator by 2 and then we will have a perfect square in the numerator and denominator, we can solve that easily.

Complete step-by-step solution:
Given,
\[\sqrt {\dfrac{{18}}{{32}}} \],
Now divide the numerator and denominator by 2,
\[ \Rightarrow \sqrt {\dfrac{{18}}{{32}}} = \sqrt {\dfrac{9}{{16}}} \]
We know that 9 and 16 are perfect square, then we have,
\[ \Rightarrow \sqrt {\dfrac{{18}}{{32}}} = \sqrt {\dfrac{{{3^2}}}{{{4^2}}}} \]
\[ \Rightarrow \dfrac{{\sqrt {{3^2}} }}{{\sqrt {{4^2}} }}\]
Square and square root will cancel out,
\[ \Rightarrow \dfrac{3}{4}\]
Thus we have,
\[ \Rightarrow \sqrt {\dfrac{{18}}{{32}}} = \dfrac{3}{4}\]. This is the exact form.
\[ \Rightarrow \sqrt {\dfrac{{18}}{{32}}} = 0.75\]. This is the decimal form.

Thus the answer is 0.75.

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.