Question

How do you simplify square root of $128$ $+$ the square root of $32$?

Answer 1

Step-1: Find the Square root of $128$.

Using prime factorization.

$\sqrt{128}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2}$

$=2\times 2\times 2\sqrt{2}$

$=8\sqrt{2}$

Step-2: Find the Square root of $32$.

Using prime factorization.

$\sqrt{32}=\sqrt{2\times 2\times 2\times 2\times 2}$

$=2\times 2\sqrt{2}$

$=4\sqrt{2}$

Step-3: Find the value of $\sqrt{128}+\sqrt{32}$.

$\sqrt{128}+\sqrt{32}$ $=8\sqrt{2}+4\sqrt{2}$ (Put the value of $\sqrt{128}$ and $\sqrt{32}$ )

$=12\sqrt{2}$

Therefore, value of $(\sqrt{128}+\sqrt{32})$ is $12\sqrt{2}$.