Solve sqrt72^2/sqrt{49sqrt{6}}

$$\frac { \sqrt { 72 } ^ { 2 } } { \sqrt { 49 } \sqrt { 6 } }$$

Evaluate

$$\frac{12\sqrt{6}}{7}\approx 4.199125273$$

Solution Steps

The square of \sqrt{72} is 72.

$$\frac{72}{\sqrt{49}\sqrt{6}}$$

Calculate the square root of 49 and get 7.

$$\frac{72}{7\sqrt{6}}$$

Rationalize the denominator of \frac{72}{7\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{72\sqrt{6}}{7\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{72\sqrt{6}}{7\times 6}$$

Cancel out 6 in both numerator and denominator.

$$\frac{12\sqrt{6}}{7}$$