Answer:
8 + 2[tex]\sqrt{15}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
[tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
Given
([tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex] )² = ([tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex] )([tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex] )
Each term in the second factor is multiplied by each term in the first factor
[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex]) + [tex]\sqrt{5}[/tex]([tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex]) ← distribute parenthesis
= 3 + [tex]\sqrt{15}[/tex] + [tex]\sqrt{15}[/tex] + 5 ← collect like terms
= 8 + 2[tex]\sqrt{15}[/tex]
