Evaluate
8
Factor
2^{3}
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\left(2\sqrt{5}-2\right)\left(\sqrt{5}+1\right)
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
2\left(\sqrt{5}\right)^{2}+2\sqrt{5}-2\sqrt{5}-2
Apply the distributive property by multiplying each term of 2\sqrt{5}-2 by each term of \sqrt{5}+1.
2\times 5+2\sqrt{5}-2\sqrt{5}-2
The square of \sqrt{5} is 5.
10+2\sqrt{5}-2\sqrt{5}-2
Multiply 2 and 5 to get 10.
10-2
Combine 2\sqrt{5} and -2\sqrt{5} to get 0.
8
Subtract 2 from 10 to get 8.
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