Question

Evaluate each expression

65. $\sqrt{\frac{4}{9}}$

Short answer

Expression $\sqrt{\frac{4}{9}}$ results into $\frac{2}{3}$

Step-by-step solution

- Meaning of ab

The symbol $\sqrt{}$is used to denote square root of a number.

Also, $\sqrt{\frac{a}{b}}$can be written as $\frac{\sqrt{a}}{\sqrt{b}}$

Thus $\sqrt{\frac{a}{b}}$denotes square root of $\text{'}a\text{'}$divided by square root of $\text{'}b\text{'}$

- Find a whole number whose square is 4

Since, $2^2=4$

So, a whole number whose square is 4 is 2

- Find a whole number whose square is 9

Since, $3^2=9$

So, a whole number whose square is 9 is 3

- Simplify 49

To simplify given expression, separate square root of both numerator and denominator terms and then simplify shown below

$\begin{array}{c}\sqrt{\frac{4}{9}}=\frac{\sqrt{4}}{\sqrt{9}}\\ =\frac{2}{3}\end{array}$

Thus, value of $\sqrt{\frac{4}{9}}$ is $\frac{2}{3}$