Solve sqrt{27/2}

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

Evaluate

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

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{2}} as the division of square roots \frac{\sqrt{27}}{\sqrt{2}}.

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

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}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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