Solve sqrt{4/3}divsqrt{3/2}

$$\sqrt { \frac { 4 } { 3 } } \div \sqrt { \frac { 3 } { 2 } }$$

Evaluate

$$\frac{2\sqrt{2}}{3}\approx 0.942809042$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{4}}{\sqrt{3}}}{\sqrt{\frac{3}{2}}}$$

Calculate the square root of 4 and get 2.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Divide \frac{2\sqrt{3}}{3} by \frac{\sqrt{6}}{2} by multiplying \frac{2\sqrt{3}}{3} by the reciprocal of \frac{\sqrt{6}}{2}.

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

Rationalize the denominator of \frac{2\sqrt{3}\times 2}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{2\sqrt{3}\times 2\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

Multiply 2 and 2 to get 4.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{3}\sqrt{2}}{3\times 6}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{4\times 3\sqrt{2}}{3\times 6}$$

Multiply 3 and 6 to get 18.

$$\frac{4\times 3\sqrt{2}}{18}$$

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{2}}{18}$$

Divide 12\sqrt{2} by 18 to get \frac{2}{3}\sqrt{2}.

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