Solve sqrt{5}*sqrt{2}div2sqrt{5}*frac{sqrt{2}}{2}

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

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

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

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

Express \frac{\sqrt{10}}{2}\sqrt{5} as a single fraction.

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

Multiply \frac{\sqrt{10}\sqrt{5}}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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}.

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

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{5\times 2}{2\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{10}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$