Solve (sqrt[10]{32})^2

$$( \sqrt[ 10 ] { 32 } ) ^ { 2 }$$

Evaluate

$$2$$

Solution Steps

Rewrite \sqrt[10]{32} as \sqrt[10]{2^{5}}. Convert from radical to exponential form and cancel out 5 in the exponent. Convert back to radical form.

$$\sqrt[10]{32}=\sqrt[10]{2^{5}}=2^{\frac{5}{10}}=2^{\frac{1}{2}}=\sqrt{2}$$

Insert the obtained value back in the expression.

$$\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2$$

Factor

$$2$$