Solve sqrt[8]{9^2}

$$\sqrt[ 8 ] { 9 ^ { 2 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\sqrt[8]{81}$$

Rewrite 81 as 3^{4}.

$$\sqrt[8]{3^{4}}$$

Convert from radical to exponential form.

$$\left(3^{4}\right)^{\frac{1}{8}}$$

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

$$3^{\frac{4}{8}}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$3^{\frac{1}{2}}$$

Convert from exponential to radical form.

$$\sqrt{3}$$