Solve sqrt{5}*sqrt{2}-3sqrt{5}*frac{sqrt{2}}{2}

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

Evaluate

$$-\frac{\sqrt{10}}{2}\approx -1.58113883$$

Solution Steps

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

$$\sqrt{10}-3\sqrt{5}\times \frac{\sqrt{2}}{2}$$

Express 3\times \frac{\sqrt{2}}{2} as a single fraction.

$$\sqrt{10}-\frac{3\sqrt{2}}{2}\sqrt{5}$$

Express \frac{3\sqrt{2}}{2}\sqrt{5} as a single fraction.

$$\sqrt{10}-\frac{3\sqrt{2}\sqrt{5}}{2}$$

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

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

Combine \sqrt{10} and -\frac{3\sqrt{10}}{2} to get -\frac{1}{2}\sqrt{10}.

$$-\frac{1}{2}\sqrt{10}$$