Solve sqrt{3}*sqrt{2/75}

$$\sqrt{ 3 } \times \sqrt{ \frac{ 2 }{ 75 } }$$

Evaluate

$$\frac{\sqrt{2}}{5}\approx 0.282842712$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{75}} as the division of square roots \frac{\sqrt{2}}{\sqrt{75}}.

$$\sqrt{3}\times \frac{\sqrt{2}}{\sqrt{75}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\sqrt{3}\times \frac{\sqrt{2}}{5\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{2}}{5\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}\times \frac{\sqrt{2}\sqrt{3}}{5\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{3}\times \frac{\sqrt{2}\sqrt{3}}{5\times 3}$$

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

$$\sqrt{3}\times \frac{\sqrt{6}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\sqrt{3}\times \frac{\sqrt{6}}{15}$$

Express \sqrt{3}\times \frac{\sqrt{6}}{15} as a single fraction.

$$\frac{\sqrt{3}\sqrt{6}}{15}$$

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}.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{2}}{15}$$

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

$$\frac{3\sqrt{2}}{15}$$

Divide 3\sqrt{2} by 15 to get \frac{1}{5}\sqrt{2}.

$$\frac{1}{5}\sqrt{2}$$