Solve (2sqrt{10}-5)(2sqrt{2}+1)=

$$( 2 \sqrt { 10 } - 5 ) ( 2 \sqrt { 2 } + 1 ) =$$

Evaluate

$$2\sqrt{10}+8\sqrt{5}-10\sqrt{2}-5\approx 5.070963517$$

Solution Steps

Apply the distributive property by multiplying each term of 2\sqrt{10}-5 by each term of 2\sqrt{2}+1.

$$4\sqrt{2}\sqrt{10}+2\sqrt{10}-10\sqrt{2}-5$$

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}.

$$4\sqrt{2}\sqrt{2}\sqrt{5}+2\sqrt{10}-10\sqrt{2}-5$$

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

$$4\times 2\sqrt{5}+2\sqrt{10}-10\sqrt{2}-5$$

Multiply 4 and 2 to get 8.

$$8\sqrt{5}+2\sqrt{10}-10\sqrt{2}-5$$