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

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

Evaluate

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

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

Express \frac{\sqrt{6}}{3}\sqrt{5} as a single fraction.

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

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

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