Solve sqrt[34]{100}

$$\sqrt[ 34 ] { 100 }$$

Evaluate

$$\sqrt[17]{10}\approx 1.14504757$$

Solution Steps

Rewrite 100 as 10^{2}.

$$\sqrt[34]{10^{2}}$$

Convert from radical to exponential form.

$$\left(10^{2}\right)^{\frac{1}{34}}$$

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

$$10^{\frac{2}{34}}$$

Reduce the fraction \frac{2}{34} to lowest terms by extracting and canceling out 2.

$$10^{\frac{1}{17}}$$

Convert from exponential to radical form.

$$\sqrt[17]{10}$$