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

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

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

Solution Steps

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

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

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}.

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

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

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

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

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

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}.

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

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

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

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

$$3\sqrt{5}$$