Solve sqrt{(1/3)^2+2^3/2^2}=

$$\sqrt { ( \frac { 1 } { 3 } ) ^ { 2 } + \frac { 2 ^ { 3 } } { 2 ^ { 2 } } } =$$

Evaluate

$$\frac{\sqrt{19}}{3}\approx 1.452966315$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\sqrt{\left(\frac{1}{3}\right)^{2}+2^{1}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\sqrt{\frac{1}{9}+2^{1}}$$

Calculate 2 to the power of 1 and get 2.

$$\sqrt{\frac{1}{9}+2}$$

Convert 2 to fraction \frac{18}{9}.

$$\sqrt{\frac{1}{9}+\frac{18}{9}}$$

Since \frac{1}{9} and \frac{18}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1+18}{9}}$$

Add 1 and 18 to get 19.

$$\sqrt{\frac{19}{9}}$$

Rewrite the square root of the division \sqrt{\frac{19}{9}} as the division of square roots \frac{\sqrt{19}}{\sqrt{9}}.

$$\frac{\sqrt{19}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{19}}{3}$$