Evaluate
24-8\sqrt{5}\approx 6.11145618
Expand
24-8\sqrt{5}
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4\left(\sqrt{5}\right)^{2}-8\sqrt{5}+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{5}-2\right)^{2}.
4\times 5-8\sqrt{5}+4
The square of \sqrt{5} is 5.
20-8\sqrt{5}+4
Multiply 4 and 5 to get 20.
24-8\sqrt{5}
Add 20 and 4 to get 24.
4\left(\sqrt{5}\right)^{2}-8\sqrt{5}+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{5}-2\right)^{2}.
4\times 5-8\sqrt{5}+4
The square of \sqrt{5} is 5.
20-8\sqrt{5}+4
Multiply 4 and 5 to get 20.
24-8\sqrt{5}
Add 20 and 4 to get 24.
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