Solve sqrt{72/2}+sqrt{17/9}

$$\sqrt { \frac { 72 } { 2 } } + \sqrt { 1 \frac { 7 } { 9 } }$$

Evaluate

$$\frac{22}{3}\approx 7.333333333$$

Solution Steps

Divide 72 by 2 to get 36.

$$\sqrt{36}+\sqrt{\frac{1\times 9+7}{9}}$$

Calculate the square root of 36 and get 6.

$$6+\sqrt{\frac{1\times 9+7}{9}}$$

Multiply 1 and 9 to get 9.

$$6+\sqrt{\frac{9+7}{9}}$$

Add 9 and 7 to get 16.

$$6+\sqrt{\frac{16}{9}}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$6+\frac{4}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{18}{3}+\frac{4}{3}$$

Since \frac{18}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{18+4}{3}$$

Add 18 and 4 to get 22.

$$\frac{22}{3}$$

Factor

$$\frac{2 \cdot 11}{3} = 7\frac{1}{3} = 7.333333333333333$$