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

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

Evaluate

$$\frac{2\sqrt{10}}{3}\approx 2.108185107$$

Solution Steps

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

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

Calculate 2 to the power of 2 and get 4.

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

Convert 4 to fraction \frac{36}{9}.

$$\sqrt{\frac{4}{9}+\frac{36}{9}}$$

Since \frac{4}{9} and \frac{36}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{4+36}{9}}$$

Add 4 and 36 to get 40.

$$\sqrt{\frac{40}{9}}$$

Rewrite the square root of the division \sqrt{\frac{40}{9}} as the division of square roots \frac{\sqrt{40}}{\sqrt{9}}.

$$\frac{\sqrt{40}}{\sqrt{9}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{2\sqrt{10}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{2\sqrt{10}}{3}$$