Evaluate
40\sqrt{2}+204\approx 260.568542495
Expand
40 \sqrt{2} + 204 = 260.568542495
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4+40\sqrt{2}+100\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-2-10\sqrt{2}\right)^{2}.
4+40\sqrt{2}+100\times 2
The square of \sqrt{2} is 2.
4+40\sqrt{2}+200
Multiply 100 and 2 to get 200.
204+40\sqrt{2}
Add 4 and 200 to get 204.
4+40\sqrt{2}+100\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-2-10\sqrt{2}\right)^{2}.
4+40\sqrt{2}+100\times 2
The square of \sqrt{2} is 2.
4+40\sqrt{2}+200
Multiply 100 and 2 to get 200.
204+40\sqrt{2}
Add 4 and 200 to get 204.
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