Solve sqrt{27}*sqrt{1/2}

$$\sqrt { 27 } \times \sqrt { \frac { 1 } { 2 } }$$

Evaluate

$$\frac{3\sqrt{6}}{2}\approx 3.674234614$$

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}.

$$3\sqrt{3}\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$3\sqrt{3}\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$3\sqrt{3}\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Express 3\times \frac{\sqrt{2}}{2} as a single fraction.

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

Express \frac{3\sqrt{2}}{2}\sqrt{3} as a single fraction.

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

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

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