Evaluate
49-24\sqrt{3}\approx 7.430780618
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49-24\sqrt{3}
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36-24\sqrt{3}+4\left(\sqrt{3}\right)^{2}+1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-2\sqrt{3}\right)^{2}.
36-24\sqrt{3}+4\times 3+1
The square of \sqrt{3} is 3.
36-24\sqrt{3}+12+1
Multiply 4 and 3 to get 12.
48-24\sqrt{3}+1
Add 36 and 12 to get 48.
49-24\sqrt{3}
Add 48 and 1 to get 49.
36-24\sqrt{3}+4\left(\sqrt{3}\right)^{2}+1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-2\sqrt{3}\right)^{2}.
36-24\sqrt{3}+4\times 3+1
The square of \sqrt{3} is 3.
36-24\sqrt{3}+12+1
Multiply 4 and 3 to get 12.
48-24\sqrt{3}+1
Add 36 and 12 to get 48.
49-24\sqrt{3}
Add 48 and 1 to get 49.
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