Solve frac{6sqrt{48}}{4sqrt{6}}

$$\frac { 6 \sqrt { 48 } } { 4 \sqrt { 6 } }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{48}}{2\sqrt{6}}$$

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}.

$$\frac{3\times 4\sqrt{3}}{2\sqrt{6}}$$

Multiply 3 and 4 to get 12.

$$\frac{12\sqrt{3}}{2\sqrt{6}}$$

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{6} is 6.

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

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}.

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

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

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

Cancel out 6 and 6.

$$3\sqrt{2}$$