Solve sqrt[8]{sqrt{1/16}+3/4}+sqrt[8]{-sqrt[3]{27}+sqrt{9}}

$$\sqrt[ 8 ] { \sqrt { \frac { 1 } { 16 } } + \frac { 3 } { 4 } } + \sqrt[ 8 ] { - \sqrt[ 3 ] { 27 } + \sqrt { 9 } }$$

Evaluate

$$1$$

Solution Steps

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\sqrt[8]{\frac{1}{4}+\frac{3}{4}}+\sqrt[8]{-\sqrt[3]{27}+\sqrt{9}}$$

Add \frac{1}{4} and \frac{3}{4} to get 1.

$$\sqrt[8]{1}+\sqrt[8]{-\sqrt[3]{27}+\sqrt{9}}$$

Calculate \sqrt[8]{1} and get 1.

$$1+\sqrt[8]{-\sqrt[3]{27}+\sqrt{9}}$$

Calculate \sqrt[3]{27} and get 3.

$$1+\sqrt[8]{-3+\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$1+\sqrt[8]{-3+3}$$

Add -3 and 3 to get 0.

$$1+\sqrt[8]{0}$$

Calculate \sqrt[8]{0} and get 0.

$$1+0$$

Add 1 and 0 to get 1.

$$1$$

Factor

$$1$$