Solve sqrt{2}(frac{sqrt{10}}{2}+frac{sqrt{10}}{4})

$$\sqrt { 2 } ( \frac { \sqrt { 10 } } { 2 } + \frac { \sqrt { 10 } } { 4 } )$$

Evaluate

$$\frac{3\sqrt{5}}{2}\approx 3.354101966$$

Solution Steps

Combine \frac{\sqrt{10}}{2} and \frac{\sqrt{10}}{4} to get \frac{3}{4}\sqrt{10}.

$$\sqrt{2}\times \frac{3}{4}\sqrt{10}$$

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

$$\sqrt{2}\times \frac{3}{4}\sqrt{2}\sqrt{5}$$

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

$$2\times \frac{3}{4}\sqrt{5}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}\sqrt{5}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}\sqrt{5}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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