Q65. - Algebra 2

Question

Evaluate each expression 

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

Step-by-Step Solution

Answer

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

Step 1 - Meaning of a b

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 $\text{'}b\text{'}$ 

Step 2 - Find a whole number whose square is 4

Since, $2^2=4$

So, a whole number whose square is 4 is 2 

Step 3 - Find a whole number whose square is 9

Since, $3^2=9$ 

So, a whole number whose square is 9 is 3

Step 4 - Simplify 4 9

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 $\frac{2}{3}$