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

$$( 3 + \sqrt { 10 } ) \times \sqrt { 2 } - \sqrt { 5 }$$

Evaluate

$$\sqrt{5}+3\sqrt{2}\approx 6.478708665$$

Solution Steps

Use the distributive property to multiply 3+\sqrt{10} by \sqrt{2}.

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

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}.

$$3\sqrt{2}+\sqrt{2}\sqrt{5}\sqrt{2}-\sqrt{5}$$

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

$$3\sqrt{2}+2\sqrt{5}-\sqrt{5}$$

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

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