Solve frac{3sqrt{10}}{10}*10/sqrt{3}

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

Evaluate

$$\sqrt{30}\approx 5.477225575$$

Solution Steps

Rationalize the denominator of \frac{10}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

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

Cancel out 3\times 10 in both numerator and denominator.

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

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

$$\sqrt{30}$$