Solve sqrt[6]{6^2-3^2}

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

Evaluate

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

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt[6]{36-3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt[6]{36-9}$$

Subtract 9 from 36 to get 27.

$$\sqrt[6]{27}$$

Rewrite 27 as 3^{3}.

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

Convert from radical to exponential form.

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

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

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

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

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

Convert from exponential to radical form.

$$\sqrt{3}$$