Question

simplify the following expressions.
$( \sqrt{3} + \sqrt{7}) {}^{2}$
$(5 + \sqrt{5} )(5 - \sqrt{5} )$

Answer 1

hi...

Hope this helps ! :)

Answer 2

( √3 + √7 )²

$\mathbf{ \textcolor{blue}{we \: \: know \: \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab }} \\ \\ \\ \\ \large{ \bf{on \: \: applying \: \: formula \: we \: get \: \: }}$

$\rightarrow {( \sqrt{3} )}^{2} + {( \sqrt{7} )}^{2} + 2( \sqrt{3} \times \sqrt{7} ) \\ \\ \rightarrow3 + 7 + 2 \sqrt{21} \\ \\ \rightarrow10 + 2 \sqrt{21} \: \: \: \: or \: \: \: 2(5 + \sqrt{21} )$



ii :



$(5 + \sqrt{5} )(5 - \sqrt{5} ) \\ \\ \\ \mathbf {\large{we \: \: know \: (a + b)(a - b) = {a}^{2} - {b}^{2} }} \\ \\ \: \\ \: \bold{applying \: \: formula}$

( 5 )² - ( √5 )²

=> 25 - 5

=> 20