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

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

Evaluate

$$\frac{\sqrt{10}}{5}\approx 0.632455532$$

Solution Steps

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\sqrt{\frac{9}{25}+\left(\frac{1}{5}\right)^{2}}$$

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

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

Since \frac{9}{25} and \frac{1}{25} have the same denominator, add them by adding their numerators.

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

Add 9 and 1 to get 10.

$$\sqrt{\frac{10}{25}}$$

Reduce the fraction \frac{10}{25} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{2}{5}}$$

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

$$\frac{\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{5}$$