Solve sqrt{3^2+4^2/125}

$$\sqrt { \frac { 3 ^ { 2 } + 4 ^ { 2 } } { 125 } }$$

Evaluate

$$\frac{\sqrt{5}}{5}\approx 0.447213595$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{\frac{9+4^{2}}{125}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{\frac{9+16}{125}}$$

Add 9 and 16 to get 25.

$$\sqrt{\frac{25}{125}}$$

Reduce the fraction \frac{25}{125} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{1}{5}}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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