Solve frac{sqrt{32}}{sqrt{1}}+sqrt[4]{16}

$$\frac { \sqrt { 32 } } { \sqrt { 1 } } + \sqrt[ 4 ] { 16 }$$

Evaluate

$$4\sqrt{2}+2\approx 7.656854249$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{32}}{\sqrt{1}} as the square root of the division \sqrt{\frac{32}{1}} and perform the division.

$$\sqrt{32}+\sqrt[4]{16}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$4\sqrt{2}+\sqrt[4]{16}$$

Calculate \sqrt[4]{16} and get 2.

$$4\sqrt{2}+2$$