Evaluate
29-12\sqrt{5}\approx 2.16718427
Expand
29-12\sqrt{5}
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4\left(\sqrt{5}\right)^{2}-12\sqrt{5}+9
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{5}-3\right)^{2}.
4\times 5-12\sqrt{5}+9
The square of \sqrt{5} is 5.
20-12\sqrt{5}+9
Multiply 4 and 5 to get 20.
29-12\sqrt{5}
Add 20 and 9 to get 29.
4\left(\sqrt{5}\right)^{2}-12\sqrt{5}+9
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{5}-3\right)^{2}.
4\times 5-12\sqrt{5}+9
The square of \sqrt{5} is 5.
20-12\sqrt{5}+9
Multiply 4 and 5 to get 20.
29-12\sqrt{5}
Add 20 and 9 to get 29.
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