Solve 2sqrt{3}divsqrt{5}*sqrt{1/5}

$$2 \sqrt{ 3 } \div \sqrt{ 5 } \times \sqrt{ \frac{ 1 }{ 5 } }$$

Evaluate

$$\frac{2\sqrt{3}}{5}\approx 0.692820323$$

Solution Steps

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

$$\frac{2\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{\frac{1}{5}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{3}\sqrt{5}}{5}\sqrt{\frac{1}{5}}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{15}}{5}\sqrt{\frac{1}{5}}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{2\sqrt{15}}{5}\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$\frac{2\sqrt{15}}{5}\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{15}}{5}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{15}}{5}\times \frac{\sqrt{5}}{5}$$

Multiply \frac{2\sqrt{15}}{5} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\sqrt{15}\sqrt{5}}{5\times 5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

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

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

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{3}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{10\sqrt{3}}{25}$$

Divide 10\sqrt{3} by 25 to get \frac{2}{5}\sqrt{3}.

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