Solve sqrt[12]{125}

$$\sqrt[ 12 ] { 125 }$$

Evaluate

$$\sqrt[4]{5}\approx 1.495348781$$

Solution Steps

Rewrite 125 as 5^{3}.

$$\sqrt[12]{5^{3}}$$

Convert from radical to exponential form.

$$\left(5^{3}\right)^{\frac{1}{12}}$$

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

$$5^{\frac{3}{12}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$5^{\frac{1}{4}}$$

Convert from exponential to radical form.

$$\sqrt[4]{5}$$