Question

simplify
$\sqrt{4 {a }^{2} + 4 \sqrt{5}ab + 5 {b}^{2} }$
​

Answer 1

Given:

$\sqrt{4 {a }^{2} + 4 \sqrt{5}ab + 5 {b}^{2} }$

to find:

Simplify

STEP BY STEP EXPLANATION:

$\sqrt{4 {a }^{2} + 4 \sqrt{5}ab + 5 {b}^{2} }$

the root of the product is equal to the product of the roots of each factor

$\sqrt{4} \sqrt{ {a}^{2} } + \sqrt[4]{5ab + 5 {b}^{2} }$

write the number in expontial form with a base of two

$\sqrt{ {2}^{2} } \sqrt{ {a}^{2} } + \sqrt[4]{5ab + 5 {b}^{2} }$

$\sqrt{ {2}^{2} } a + 4 \sqrt{5ab + 5 {b}^{2} }$

reduce the index of the radical and exponent with 2

$2a + 4 \sqrt{5ab + 5 {b}^{2} }$