Solve (2)sqrt{3/3}divsqrt{3/2}=

$$( 2 ) \sqrt { \frac { 3 } { 3 } } \div \sqrt { \frac { 3 } { 2 } } =$$

Evaluate

$$\frac{2\sqrt{6}}{3}\approx 1.632993162$$

Solution Steps

Divide 3 by 3 to get 1.

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

Calculate the square root of 1 and get 1.

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

Multiply 2 and 1 to get 2.

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

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Divide 2 by \frac{\sqrt{6}}{2} by multiplying 2 by the reciprocal of \frac{\sqrt{6}}{2}.

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

Rationalize the denominator of \frac{2\times 2}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{2\times 2\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

Multiply 2 and 2 to get 4.

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

Divide 4\sqrt{6} by 6 to get \frac{2}{3}\sqrt{6}.

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