Solve sqrt{5^2/25+3^2/36}

$$\sqrt { \frac { 5 ^ { 2 } } { 25 } + \frac { 3 ^ { 2 } } { 36 } }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{25}{25}+\frac{3^{2}}{36}}$$

Divide 25 by 25 to get 1.

$$\sqrt{1+\frac{3^{2}}{36}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{1+\frac{9}{36}}$$

Reduce the fraction \frac{9}{36} to lowest terms by extracting and canceling out 9.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

$$\sqrt{\frac{5}{4}}$$

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

$$\frac{\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

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