Solve sqrt[3]{(5^2+4^3)^2/sqrt{25}}

$$\sqrt[ 3 ] { \frac { ( 5 ^ { 2 } + 4 ^ { 3 } ) ^ { 2 } } { \sqrt { 25 } } }$$

Evaluate

$$\frac{445^{\frac{2}{3}}}{5}\approx 11.657443958$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt[3]{\frac{\left(25+4^{3}\right)^{2}}{\sqrt{25}}}$$

Calculate 4 to the power of 3 and get 64.

$$\sqrt[3]{\frac{\left(25+64\right)^{2}}{\sqrt{25}}}$$

Add 25 and 64 to get 89.

$$\sqrt[3]{\frac{89^{2}}{\sqrt{25}}}$$

Calculate 89 to the power of 2 and get 7921.

$$\sqrt[3]{\frac{7921}{\sqrt{25}}}$$

Calculate the square root of 25 and get 5.

$$\sqrt[3]{\frac{7921}{5}}$$