Solve frac{24sqrt{72}}{3sqrt{2}}

$$\frac { 24 \sqrt { 72 } } { 3 \sqrt { 2 } }$$

Evaluate

$$48$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{8\sqrt{72}}{\sqrt{2}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{8\times 6\sqrt{2}}{\sqrt{2}}$$

Multiply 8 and 6 to get 48.

$$\frac{48\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{48\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{48\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{48\sqrt{2}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{48\times 2}{2}$$

Multiply 48 and 2 to get 96.

$$\frac{96}{2}$$

Divide 96 by 2 to get 48.

$$48$$

Factor

$$2^{4}\times 3$$