Solve frac{15sqrt{24}}{5sqrt{3}}

$$\frac { 15 \sqrt { 24 } } { 5 \sqrt { 3 } }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Cancel out 5 in both numerator and denominator.

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

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{6}}{\sqrt{3}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{6}}{\sqrt{3}}$$

Rationalize the denominator of \frac{6\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{6\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{6}\sqrt{3}}{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{6\sqrt{3}\sqrt{2}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{6\times 3\sqrt{2}}{3}$$

Cancel out 3 and 3.

$$6\sqrt{2}$$