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

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

Evaluate

$$-\sqrt{5}-2\sqrt{2}\approx -5.064495102$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{10}+3 by each term of \sqrt{2}-\sqrt{5}.

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

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}.

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

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

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

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}.

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

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

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

Combine -5\sqrt{2} and 3\sqrt{2} to get -2\sqrt{2}.

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

Combine 2\sqrt{5} and -3\sqrt{5} to get -\sqrt{5}.

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