Solve sqrt{27/8}

$$\sqrt { \frac { 27 } { 8 } }$$

Evaluate

$$\frac{3\sqrt{6}}{4}\approx 1.837117307$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{8}} as the division of square roots \frac{\sqrt{27}}{\sqrt{8}}.

$$\frac{\sqrt{27}}{\sqrt{8}}$$

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}.

$$\frac{3\sqrt{3}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 2 and 2 to get 4.

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