Solve sqrt[10]{32}

$$\sqrt[ 10 ] { 32 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Rewrite 32 as 2^{5}.

$$\sqrt[10]{2^{5}}$$

Convert from radical to exponential form.

$$\left(2^{5}\right)^{\frac{1}{10}}$$

To raise a power to another power, multiply the exponents.

$$2^{\frac{5}{10}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$2^{\frac{1}{2}}$$

Convert from exponential to radical form.

$$\sqrt{2}$$