Solve sqrt{(48/5)^2+5^2}

$$\sqrt { ( \frac { 48 } { 5 } ) ^ { 2 } + 5 ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{2929}}{5}\approx 10.824047302$$

Solution Steps

Calculate \frac{48}{5} to the power of 2 and get \frac{2304}{25}.

$$\sqrt{\frac{2304}{25}+5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{2304}{25}+25}$$

Convert 25 to fraction \frac{625}{25}.

$$\sqrt{\frac{2304}{25}+\frac{625}{25}}$$

Since \frac{2304}{25} and \frac{625}{25} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{2304+625}{25}}$$

Add 2304 and 625 to get 2929.

$$\sqrt{\frac{2929}{25}}$$

Rewrite the square root of the division \sqrt{\frac{2929}{25}} as the division of square roots \frac{\sqrt{2929}}{\sqrt{25}}.

$$\frac{\sqrt{2929}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{\sqrt{2929}}{5}$$