Solve frac{sqrt{27*6}}{sqrt{3}}

$$\frac{ \sqrt{ 27 \times 6 } }{ \sqrt{ 3 } }$$

Evaluate

$$3\sqrt{6}\approx 7.348469228$$

Solution Steps

Multiply 27 and 6 to get 162.

$$\frac{\sqrt{162}}{\sqrt{3}}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$\frac{9\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{9\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{9\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{9\sqrt{2}\sqrt{3}}{3}$$

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

$$\frac{9\sqrt{6}}{3}$$

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

$$3\sqrt{6}$$