Solve (sqrt{2}*sqrt{15}-3sqrt{30})divsqrt{3}=

$$( \sqrt { 2 } \times \sqrt { 15 } - 3 \sqrt { 30 } ) \div \sqrt { 3 } =$$

Evaluate

$$-2\sqrt{10}\approx -6.32455532$$

Solution Steps

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

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

Combine \sqrt{30} and -3\sqrt{30} to get -2\sqrt{30}.

$$\frac{-2\sqrt{30}}{\sqrt{3}}$$

Rationalize the denominator of \frac{-2\sqrt{30}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-2\sqrt{30}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{-2\sqrt{30}\sqrt{3}}{3}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{-2\sqrt{3}\sqrt{10}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-2\times 3\sqrt{10}}{3}$$

Cancel out 3 and 3.

$$-2\sqrt{10}$$