Evaluate
49-12\sqrt{5}\approx 22.16718427
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49-12\sqrt{5}
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9\left(\sqrt{5}\right)^{2}-12\sqrt{5}+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3\sqrt{5}-2\right)^{2}.
9\times 5-12\sqrt{5}+4
The square of \sqrt{5} is 5.
45-12\sqrt{5}+4
Multiply 9 and 5 to get 45.
49-12\sqrt{5}
Add 45 and 4 to get 49.
9\left(\sqrt{5}\right)^{2}-12\sqrt{5}+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3\sqrt{5}-2\right)^{2}.
9\times 5-12\sqrt{5}+4
The square of \sqrt{5} is 5.
45-12\sqrt{5}+4
Multiply 9 and 5 to get 45.
49-12\sqrt{5}
Add 45 and 4 to get 49.
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