Evaluate
69-12\sqrt{15}\approx 22.524199846
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69-12\sqrt{15}
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9-12\sqrt{15}+4\left(\sqrt{15}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-2\sqrt{15}\right)^{2}.
9-12\sqrt{15}+4\times 15
The square of \sqrt{15} is 15.
9-12\sqrt{15}+60
Multiply 4 and 15 to get 60.
69-12\sqrt{15}
Add 9 and 60 to get 69.
9-12\sqrt{15}+4\left(\sqrt{15}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-2\sqrt{15}\right)^{2}.
9-12\sqrt{15}+4\times 15
The square of \sqrt{15} is 15.
9-12\sqrt{15}+60
Multiply 4 and 15 to get 60.
69-12\sqrt{15}
Add 9 and 60 to get 69.
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