Solve sqrt{7}:sqrt{81/7}

$$\sqrt { 7 } : \sqrt { \frac { 81 } { 7 } }$$

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{81}{7}} as the division of square roots \frac{\sqrt{81}}{\sqrt{7}}.

$$\frac{\sqrt{7}}{\frac{\sqrt{81}}{\sqrt{7}}}$$

Calculate the square root of 81 and get 9.

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

Rationalize the denominator of \frac{9}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{7}}{\frac{9\sqrt{7}}{\left(\sqrt{7}\right)^{2}}}$$

The square of \sqrt{7} is 7.

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

Divide \sqrt{7} by \frac{9\sqrt{7}}{7} by multiplying \sqrt{7} by the reciprocal of \frac{9\sqrt{7}}{7}.

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

Cancel out \sqrt{7} in both numerator and denominator.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$