Simplify the following expressions:$ (\sqrt{5}-\sqrt{3})^{2} $

Given:

\( (\sqrt{5}-\sqrt{3})^{2} \)

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,

$(\sqrt{5}-\sqrt{3})^{2}=(\sqrt{5})^{2}+(\sqrt{3})^{2}-2 \times \sqrt{5} \times \sqrt{3}$

$=5+3-2 \sqrt{5\times3}$

$=8-2 \sqrt{15}$

Hence, $(\sqrt{5}-\sqrt{3})^{2}=8-2 \sqrt{15}$. 

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Updated on: 10-Oct-2022

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