Solve sqrt[8]{2^2}-8^2

$$\sqrt[ 8 ] { 2 ^ { 2 } } - 8 ^ { 2 }$$

Evaluate

$$\sqrt[4]{2}-64\approx -62.810792885$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\sqrt[8]{4}-8^{2}$$

Rewrite \sqrt[8]{4} as \sqrt[8]{2^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[8]{4}=\sqrt[8]{2^{2}}=2^{\frac{2}{8}}=2^{\frac{1}{4}}=\sqrt[4]{2}$$

Insert the obtained value back in the expression.

$$\sqrt[4]{2}-8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt[4]{2}-64$$