Solve sqrt{27}*sqrt{55}divsqrt{6}

$$\sqrt { 27 } \times \sqrt { 55 } \div \sqrt { 6 }$$

Evaluate

$$\frac{3\sqrt{110}}{2}\approx 15.732132723$$

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}.

$$\frac{3\sqrt{3}\sqrt{55}}{\sqrt{6}}$$

To multiply \sqrt{3} and \sqrt{55}, multiply the numbers under the square root.

$$\frac{3\sqrt{165}}{\sqrt{6}}$$

Rationalize the denominator of \frac{3\sqrt{165}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{3\sqrt{165}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{3\sqrt{165}\sqrt{6}}{6}$$

To multiply \sqrt{165} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{3\sqrt{990}}{6}$$

Factor 990=3^{2}\times 110. Rewrite the square root of the product \sqrt{3^{2}\times 110} as the product of square roots \sqrt{3^{2}}\sqrt{110}. Take the square root of 3^{2}.

$$\frac{3\times 3\sqrt{110}}{6}$$

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{110}}{6}$$

Divide 9\sqrt{110} by 6 to get \frac{3}{2}\sqrt{110}.

$$\frac{3}{2}\sqrt{110}$$