Evaluate
5\sqrt{2}+8\approx 15.071067812
Factor
5 \sqrt{2} + 8 = 15.071067812
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\left(\sqrt{2}\right)^{2}+2\sqrt{2}+3\sqrt{2}+6
Apply the distributive property by multiplying each term of \sqrt{2}+3 by each term of \sqrt{2}+2.
2+2\sqrt{2}+3\sqrt{2}+6
The square of \sqrt{2} is 2.
2+5\sqrt{2}+6
Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.
8+5\sqrt{2}
Add 2 and 6 to get 8.
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