Solve frac{sqrt{2}}{sqrt{5}}*frac{(sqrt{5})^2}{sqrt{3}}

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

Evaluate

$$\frac{\sqrt{30}}{3}\approx 1.825741858$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

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

$$\frac{\sqrt{10}}{5}\times \frac{\left(\sqrt{5}\right)^{2}}{\sqrt{3}}$$

The square of \sqrt{5} is 5.

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

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

$$\frac{\sqrt{10}}{5}\times \frac{5\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Multiply \frac{\sqrt{10}}{5} times \frac{5\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{3}$$