Question

Simplify $\sqrt{128}+\sqrt{32}$

Answer 1

Simplify the given expression:

$\sqrt{128}+\sqrt{32}={\left(128\right)}^{\frac{1}{2}}+{\left(32\right)}^{\frac{1}{2}}$

$$\begin{gathered} ={\left(2^7\right)}^{\frac{1}{2}}+{\left(2^5\right)}^{\frac{1}{2}} \\ =2^{\frac{7}{2}}+2^{\frac{5}{2}}\left[\because {\left(a^m\right)}^n=a^{mn}\right] \\ =2^{3.5}+2^{2.5} \\ =2^3·2^{\frac{1}{2}}+2^2·2^{\frac{1}{2}}\left[\because a^{m+n}=a^m{a}^n\right] \\ =2^{\frac{1}{2}}\left(8+4\right) \\ =12\sqrt{2} \end{gathered}$$

Hence, the simplified form is $12\sqrt{2}$