Solve sqrt{left(4+5right)^2+4^2/sqrt{4+5}}

$$\sqrt{ \frac{ { \left(4+5 \right) }^{ 2 } + { 4 }^{ 2 } }{ \sqrt{ 4+5 } } }$$

Evaluate

$$\frac{\sqrt{291}}{3}\approx 5.686240703$$

Solution Steps

Add 4 and 5 to get 9.

$$\sqrt{\frac{9^{2}+4^{2}}{\sqrt{4+5}}}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{\frac{81+4^{2}}{\sqrt{4+5}}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{\frac{81+16}{\sqrt{4+5}}}$$

Add 81 and 16 to get 97.

$$\sqrt{\frac{97}{\sqrt{4+5}}}$$

Add 4 and 5 to get 9.

$$\sqrt{\frac{97}{\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

$$\sqrt{\frac{97}{3}}$$

Rewrite the square root of the division \sqrt{\frac{97}{3}} as the division of square roots \frac{\sqrt{97}}{\sqrt{3}}.

$$\frac{\sqrt{97}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{97}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{97}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{97}\sqrt{3}}{3}$$

To multiply \sqrt{97} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{291}}{3}$$