Question

Evaluate each expression

$\sqrt{\frac{36}{49}}$

Short answer

Expression $\sqrt{\frac{36}{49}}$ results into $\frac{6}{7}$

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, $6^2=36$

So, a whole number whose square is 36 is 6

- Find a whole number whose square is 9

Since, $7^2=49$

So, a whole number whose square is 49 is 7

- Simplify 3649

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

$\begin{array}{c}\sqrt{\frac{36}{49}}=\frac{\sqrt{36}}{\sqrt{49}}\\ =\frac{6}{7}\end{array}$

Thus, value of $\sqrt{\frac{36}{49}}$ is $\frac{6}{7}$