Solve sqrt{9/7}*sqrt{56/72}=

$$\sqrt { \frac { 9 } { 7 } } \cdot \sqrt { \frac { 56 } { 72 } } =$$

Evaluate

$$1$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{9}{7}} as the division of square roots \frac{\sqrt{9}}{\sqrt{7}}.

$$\frac{\sqrt{9}}{\sqrt{7}}\sqrt{\frac{56}{72}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{7}}\sqrt{\frac{56}{72}}$$

Rationalize the denominator of \frac{3}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{3\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\sqrt{\frac{56}{72}}$$

The square of \sqrt{7} is 7.

$$\frac{3\sqrt{7}}{7}\sqrt{\frac{56}{72}}$$

Reduce the fraction \frac{56}{72} to lowest terms by extracting and canceling out 8.

$$\frac{3\sqrt{7}}{7}\sqrt{\frac{7}{9}}$$

Rewrite the square root of the division \sqrt{\frac{7}{9}} as the division of square roots \frac{\sqrt{7}}{\sqrt{9}}.

$$\frac{3\sqrt{7}}{7}\times \frac{\sqrt{7}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{3\sqrt{7}}{7}\times \frac{\sqrt{7}}{3}$$

Multiply \frac{3\sqrt{7}}{7} times \frac{\sqrt{7}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{7}\sqrt{7}}{7\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{7}\sqrt{7}}{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$1$$

Factor

$$1$$