Solve sqrt{5}*(frac{sqrt{2}}{sqrt{5}}-3*sqrt{10})=

$$\sqrt { 5 } \cdot ( \frac { \sqrt { 2 } } { \sqrt { 5 } } - 3 \cdot \sqrt { 10 } ) =$$

Evaluate

$$-14\sqrt{2}\approx -19.798989873$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

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

$$\sqrt{5}\left(\frac{\sqrt{10}}{5}-3\sqrt{10}\right)$$

Combine \frac{\sqrt{10}}{5} and -3\sqrt{10} to get -\frac{14}{5}\sqrt{10}.

$$\sqrt{5}\left(-\frac{14}{5}\right)\sqrt{10}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\sqrt{5}\left(-\frac{14}{5}\right)\sqrt{5}\sqrt{2}$$

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

$$5\left(-\frac{14}{5}\right)\sqrt{2}$$

Cancel out 5 and 5.

$$-14\sqrt{2}$$