Question

Expand (root 3+ root 2)^4

Answer 1

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Answer 2

The expansion of $(\sqrt{3}+\sqrt{2})^{4}$ is $49+20\sqrt{6}$.

Step-by-step explanation:

We have,

$(\sqrt{3}+\sqrt{2})^{4}$

To expand the $(\sqrt{3}+\sqrt{2})^{4}=?$

∴ $((\sqrt{3}+\sqrt{2})^{2})^{2}$

$=[(\sqrt{3})^{2} +(\sqrt{2})^{2}+2(\sqrt{3})(\sqrt{2})]^{2}$

[ ∵ $(a+b)^{2} =a^{2} +2ab+b^{2}$]

$=(3 +2+2\sqrt{6})^{2}$

$=(5+2\sqrt{6})^{2}$

$=5^{2}+(2\sqrt{6})^{2}+2(5)(2\sqrt{6})$

$=25+4(6)+20\sqrt{6}$

$=25+24+20\sqrt{6}$

$=49+20\sqrt{6}$

Hence, the expansion of $(\sqrt{3}+\sqrt{2})^{4}$ is $49+20\sqrt{6}$.