Solve 3sqrt{5}div6sqrt{2/5}

$$3 \sqrt { 5 } \div 6 \sqrt { \frac { 2 } { 5 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Divide 3\sqrt{5} by 6 to get \frac{1}{2}\sqrt{5}.

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

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

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

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

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{10}}{5}$$

Multiply \frac{1}{2} times \frac{\sqrt{10}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{10}}{2\times 5}\sqrt{5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{10}}{10}\sqrt{5}$$

Express \frac{\sqrt{10}}{10}\sqrt{5} as a single fraction.

$$\frac{\sqrt{10}\sqrt{5}}{10}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{\sqrt{5}\sqrt{2}\sqrt{5}}{10}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\sqrt{2}}{10}$$

Divide 5\sqrt{2} by 10 to get \frac{1}{2}\sqrt{2}.

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