Solve sqrt{frac{8/9}}{frac{sqrt{8}}{9}}=

$$\frac { \sqrt { \frac { 8 } { 9 } } } { \frac { \sqrt { 8 } } { 9 } } =$$

Evaluate

$$3$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{9}} as the division of square roots \frac{\sqrt{8}}{\sqrt{9}}.

$$\frac{\frac{\sqrt{8}}{\sqrt{9}}}{\frac{\sqrt{8}}{9}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\frac{2\sqrt{2}}{\sqrt{9}}}{\frac{\sqrt{8}}{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\frac{2\sqrt{2}}{3}}{\frac{\sqrt{8}}{9}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\frac{2\sqrt{2}}{3}}{\frac{2\sqrt{2}}{9}}$$

Divide \frac{2\sqrt{2}}{3} by \frac{2\sqrt{2}}{9} by multiplying \frac{2\sqrt{2}}{3} by the reciprocal of \frac{2\sqrt{2}}{9}.

$$\frac{2\sqrt{2}\times 9}{3\times 2\sqrt{2}}$$

Cancel out 2\times 3\sqrt{2} in both numerator and denominator.

$$3$$

Factor

$$3$$