Evaluate
10\sqrt{2}+27\approx 41.142135624
Expand
10 \sqrt{2} + 27 = 41.142135624
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25+10\sqrt{2}+\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5+\sqrt{2}\right)^{2}.
25+10\sqrt{2}+2
The square of \sqrt{2} is 2.
27+10\sqrt{2}
Add 25 and 2 to get 27.
25+10\sqrt{2}+\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5+\sqrt{2}\right)^{2}.
25+10\sqrt{2}+2
The square of \sqrt{2} is 2.
27+10\sqrt{2}
Add 25 and 2 to get 27.
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