Solve sqrt[6]{sqrt{15^4}}

$$\sqrt[ 6 ] { \sqrt { 15 ^ { 4 } } }$$

Evaluate

$$\sqrt[3]{15}\approx 2.466212074$$

Solution Steps

Calculate 15 to the power of 4 and get 50625.

$$\sqrt[6]{\sqrt{50625}}$$

Calculate the square root of 50625 and get 225.

$$\sqrt[6]{225}$$

Rewrite 225 as 15^{2}.

$$\sqrt[6]{15^{2}}$$

Convert from radical to exponential form.

$$\left(15^{2}\right)^{\frac{1}{6}}$$

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

$$15^{\frac{2}{6}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$15^{\frac{1}{3}}$$

Convert from exponential to radical form.

$$\sqrt[3]{15}$$