Solve sqrt{(3/5)^2+(6/5)^2}

$$\sqrt { ( \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 6 } { 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{5}}{5}\approx 1.341640786$$

Solution Steps

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

$$\sqrt{\frac{9}{25}+\left(\frac{6}{5}\right)^{2}}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\sqrt{\frac{9}{25}+\frac{36}{25}}$$

Since \frac{9}{25} and \frac{36}{25} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{9+36}{25}}$$

Add 9 and 36 to get 45.

$$\sqrt{\frac{45}{25}}$$

Reduce the fraction \frac{45}{25} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{9}{5}}$$

Rewrite the square root of the division \sqrt{\frac{9}{5}} as the division of square roots \frac{\sqrt{9}}{\sqrt{5}}.

$$\frac{\sqrt{9}}{\sqrt{5}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{5}}$$

Rationalize the denominator of \frac{3}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{5}}{5}$$