Solve sqrt{5}*(sqrt{10}+sqrt{5})-5/2*sqrt{8}

$$\sqrt { 5 } \cdot ( \sqrt { 10 } + \sqrt { 5 } ) - \frac { 5 } { 2 } \cdot \sqrt { 8 }$$

Evaluate

$$5$$

Solution Steps

Use the distributive property to multiply \sqrt{5} by \sqrt{10}+\sqrt{5}.

$$\sqrt{5}\sqrt{10}+\left(\sqrt{5}\right)^{2}-\frac{5}{2}\sqrt{8}$$

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}.

$$\sqrt{5}\sqrt{5}\sqrt{2}+\left(\sqrt{5}\right)^{2}-\frac{5}{2}\sqrt{8}$$

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

$$5\sqrt{2}+\left(\sqrt{5}\right)^{2}-\frac{5}{2}\sqrt{8}$$

The square of \sqrt{5} is 5.

$$5\sqrt{2}+5-\frac{5}{2}\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Cancel out 2 and 2.

$$5\sqrt{2}+5-5\sqrt{2}$$

Combine 5\sqrt{2} and -5\sqrt{2} to get 0.

$$5$$

Factor

$$5$$