Simplify the following expressions:$ (\sqrt{3}+\sqrt{7})^{2} $

Given:

\( (\sqrt{3}+\sqrt{7})^{2} \)

To do: 

We have to simplify the given expression.

Solution:

We know that,

$(a+b)(a-b)=a^2-b^2$

$(a+b)^2=a^2+2ab+b^2$

$(a-b)^2=a^2-2ab+b^2$

Therefore,

$(\sqrt{3}+\sqrt{7})^{2}=(\sqrt{3})^{2}+(\sqrt{7})^{2}+2 \times \sqrt{3} \times \sqrt{7}$

$=3+7+2 \sqrt{3\times7}$

$=10+2 \sqrt{21}$

Hence, $(\sqrt{3}+\sqrt{7})^{2}=10+2 \sqrt{21}$.

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Updated on: 10-Oct-2022

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