Evaluate
84-30\sqrt{3}\approx 32.038475773
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84-30\sqrt{3}
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9-30\sqrt{3}+25\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-5\sqrt{3}\right)^{2}.
9-30\sqrt{3}+25\times 3
The square of \sqrt{3} is 3.
9-30\sqrt{3}+75
Multiply 25 and 3 to get 75.
84-30\sqrt{3}
Add 9 and 75 to get 84.
9-30\sqrt{3}+25\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-5\sqrt{3}\right)^{2}.
9-30\sqrt{3}+25\times 3
The square of \sqrt{3} is 3.
9-30\sqrt{3}+75
Multiply 25 and 3 to get 75.
84-30\sqrt{3}
Add 9 and 75 to get 84.
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