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

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

Evaluate

$$\frac{4\sqrt{5}}{3}\approx 2.98142397$$

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, subtract them by subtracting their numerators.

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

Subtract 64 from 144 to get 80.

$$\sqrt{\frac{80}{9}}$$

Rewrite the square root of the division \sqrt{\frac{80}{9}} as the division of square roots \frac{\sqrt{80}}{\sqrt{9}}.

$$\frac{\sqrt{80}}{\sqrt{9}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{4\sqrt{5}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{4\sqrt{5}}{3}$$