Solve =sqrt{900/16+144/9}

$$= \sqrt { \frac { 900 } { 16 } + \frac { 144 } { 9 } }$$

Evaluate

$$\frac{17}{2}=8.5$$

Solution Steps

Reduce the fraction \frac{900}{16} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{225}{4}+\frac{144}{9}}$$

Divide 144 by 9 to get 16.

$$\sqrt{\frac{225}{4}+16}$$

Convert 16 to fraction \frac{64}{4}.

$$\sqrt{\frac{225}{4}+\frac{64}{4}}$$

Since \frac{225}{4} and \frac{64}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{225+64}{4}}$$

Add 225 and 64 to get 289.

$$\sqrt{\frac{289}{4}}$$

Rewrite the square root of the division \frac{289}{4} as the division of square roots \frac{\sqrt{289}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{17}{2}$$

Factor

$$\frac{17}{2} = 8\frac{1}{2} = 8.5$$