Question

Simplify, choosing the correct answer as a mixed number in lowest terms. sqrt of 400/49

Answer 1

we are given

$\sqrt{\frac{400}{49}}$

we can write it as

$=\frac{\sqrt{400}}{\sqrt{49}}$

now, we can factor top and bottom

$=\frac{\sqrt{20*20}}{\sqrt{7*7}}$

$=\frac{\sqrt{20^2}}{\sqrt{7^2}}$

now, we can simplify it

we get

$=\frac{20}{7}$

now, we can change in mixed form

$=2\frac{6}{7}$...............Answer

Answer 2

$\sqrt{\dfrac{400}{49}}=\dfrac{\sqrt{400}}{\sqrt{49}}=\dfrac{20}{7}=2\dfrac{6}{7}\\\\\text{Used}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{400}=20\ \text{because}\ 20^2=400\\\\\sqrt{49}=7\ \text{because}\ 7^2=49$