Answer:
4
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
Given
([tex]\sqrt{3}[/tex] + [tex]\sqrt{7}[/tex] )([tex]\sqrt{7}[/tex] - [tex]\sqrt{3}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
[tex]\sqrt{3}[/tex] ([tex]\sqrt{7}[/tex] - [tex]\sqrt{3}[/tex] ) + [tex]\sqrt{7}[/tex] ([tex]\sqrt{7}[/tex] - [tex]\sqrt{3}[/tex] ) ← distribute both parenthesis
= [tex]\sqrt{21}[/tex] - 3 + 7 - [tex]\sqrt{21}[/tex] ← collect like terms
= 4
