Solve sqrt{4^2+(8/3)^2}

$$\sqrt { 4 ^ { 2 } + ( \frac { 8 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{4\sqrt{13}}{3}\approx 4.807401701$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16+\left(\frac{8}{3}\right)^{2}}$$

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\sqrt{16+\frac{64}{9}}$$

Convert 16 to fraction \frac{144}{9}.

$$\sqrt{\frac{144}{9}+\frac{64}{9}}$$

Since \frac{144}{9} and \frac{64}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{144+64}{9}}$$

Add 144 and 64 to get 208.

$$\sqrt{\frac{208}{9}}$$

Rewrite the square root of the division \sqrt{\frac{208}{9}} as the division of square roots \frac{\sqrt{208}}{\sqrt{9}}.

$$\frac{\sqrt{208}}{\sqrt{9}}$$

Factor 208=4^{2}\times 13. Rewrite the square root of the product \sqrt{4^{2}\times 13} as the product of square roots \sqrt{4^{2}}\sqrt{13}. Take the square root of 4^{2}.

$$\frac{4\sqrt{13}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{4\sqrt{13}}{3}$$