Solve frac{sqrt{27}sqrt{32}}{sqrt{6}}

$$\frac{ \sqrt{ 27 } \sqrt{ 32 } }{ \sqrt{ 6 } }$$

Evaluate

$$12$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3\sqrt{3}\sqrt{32}}{\sqrt{6}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Multiply 3 and 4 to get 12.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Rationalize the denominator of \frac{12\sqrt{6}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{12\sqrt{6}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{12\times 6}{6}$$

Multiply 12 and 6 to get 72.

$$\frac{72}{6}$$

Divide 72 by 6 to get 12.

$$12$$

Factor

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