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

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

Evaluate

$$\frac{\sqrt{10}}{3}\approx 1.054092553$$

Solution Steps

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

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

Calculate 1 to the power of 2 and get 1.

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

Convert 1 to fraction \frac{9}{9}.

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

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

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

Add 1 and 9 to get 10.

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

Rewrite the square root of the division \sqrt{\frac{10}{9}} as the division of square roots \frac{\sqrt{10}}{\sqrt{9}}.

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

Calculate the square root of 9 and get 3.

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