Solve 3/2sqrt{8/3}=

$$\frac { 3 } { 2 } \sqrt { \frac { 8 } { 3 } } =$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{3}{2}\times \frac{\sqrt{8}}{\sqrt{3}}$$

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}.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply \frac{3}{2} times \frac{2\sqrt{6}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2\times 3 in both numerator and denominator.

$$\sqrt{6}$$