Solve frac{6sqrt{48}}{3sqrt{3}}

$$\frac { 6 \sqrt { 48 } } { 3 \sqrt { 3 } }$$

Evaluate

$$8$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{48}}{\sqrt{3}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{2\times 4\sqrt{3}}{\sqrt{3}}$$

Multiply 2 and 4 to get 8.

$$\frac{8\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{8\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{8\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{8\sqrt{3}\sqrt{3}}{3}$$

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

$$\frac{8\times 3}{3}$$

Multiply 8 and 3 to get 24.

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

Divide 24 by 3 to get 8.

$$8$$

Factor

$$2^{3}$$