Solve sqrt[6]{8}

$$\sqrt[ 6 ] { 8 }$$

Evaluate

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

Solution Steps

Rewrite 8 as 2^{3}.

$$\sqrt[6]{2^{3}}$$

Convert from radical to exponential form.

$$\left(2^{3}\right)^{\frac{1}{6}}$$

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

$$2^{\frac{3}{6}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Convert from exponential to radical form.

$$\sqrt{2}$$