Simplify square root of 2ab+ fourth root of 4a^2b^2

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

Step 1

Simplify each term.

Rewrite $4 a^{2} b^{2}$ as ${(2 a b)}^{2}$ .

$\sqrt{2 a b} + \sqrt[4]{{(2 a b)}^{2}}$

Rewrite $\sqrt[4]{{(2 a b)}^{2}}$ as $\sqrt{\sqrt{{(2 a b)}^{2}}}$ .

$\sqrt{2 a b} + \sqrt{\sqrt{{(2 a b)}^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{2 a b} + \sqrt{2 a b}$

Step 2

Add $\sqrt{2 a b}$ and $\sqrt{2 a b}$ .

$2 \sqrt{2 a b}$