Solve sqrt{(-1/5)^2+(2/3)^2}

$$\sqrt { ( - \frac { 1 } { 5 } ) ^ { 2 } + ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{109}}{15}\approx 0.696020434$$

Solution Steps

Calculate -\frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\sqrt{\frac{1}{25}+\left(\frac{2}{3}\right)^{2}}$$

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

$$\sqrt{\frac{1}{25}+\frac{4}{9}}$$

Least common multiple of 25 and 9 is 225. Convert \frac{1}{25} and \frac{4}{9} to fractions with denominator 225.

$$\sqrt{\frac{9}{225}+\frac{100}{225}}$$

Since \frac{9}{225} and \frac{100}{225} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{9+100}{225}}$$

Add 9 and 100 to get 109.

$$\sqrt{\frac{109}{225}}$$

Rewrite the square root of the division \sqrt{\frac{109}{225}} as the division of square roots \frac{\sqrt{109}}{\sqrt{225}}.

$$\frac{\sqrt{109}}{\sqrt{225}}$$

Calculate the square root of 225 and get 15.

$$\frac{\sqrt{109}}{15}$$