Question

simplify the following expression (5+√7) (5-√7)​

Answer 1

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$\rightarrow{(5\:+\:\sqrt{7})\:(5\:-\:\sqrt{7})}$

$\rightarrow{5\:(5\:-\:\sqrt{7})\:+\:\sqrt{7}(5\:-\:\sqrt{7})}$

$\rightarrow{25\:-\:5\sqrt{7}\:+\:5\sqrt{7}\:-\:7}$

$\rightarrow{25\:-\:7}$

$\rightarrow{18}$

Answer 2

Given,

$(5+\sqrt{7} )(5-\sqrt{7} )$

Given expression is in the form of $(a+b)(a-b)$, this can be written as $(a^{2}-b^{2})$

Here,

$a= 5$

$b=\sqrt{7}$

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

$(5+\sqrt{7} )(5-\sqrt{7} )=5^{2} -(\sqrt{7} )^{2}$

$= 25-7\\=18$

Therefore, the answer is $18$.