Question
Simplify the following expression:
$(2\sqrt{5}+3\sqrt{2})^2$
$(2\sqrt{5}+3\sqrt{2})^2$
✓
Answer
$(2\sqrt{5}+3\sqrt{2})^2$
As we know, $(a+b)^2=\left(a^2+2 \times b+b^2\right)$
$=4\sqrt{5\times5}+2\times2\sqrt{5}\times3\sqrt{2}+9\sqrt{2\times2}$
$=20+12\sqrt{10}+18$
$=38+12\sqrt{10}$
As we know, $(a+b)^2=\left(a^2+2 \times b+b^2\right)$
$=4\sqrt{5\times5}+2\times2\sqrt{5}\times3\sqrt{2}+9\sqrt{2\times2}$
$=20+12\sqrt{10}+18$
$=38+12\sqrt{10}$
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