Answer:
11 + 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Note that [tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 5
Given
(3 + [tex]\sqrt{5}[/tex] )(2 + [tex]\sqrt{5}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
3(2 + [tex]\sqrt{5}[/tex] ) + [tex]\sqrt{5}[/tex](2 + [tex]\sqrt{5}[/tex] ) ← distribute both parenthesis
= 6 + 3[tex]\sqrt{5}[/tex] + 2[tex]\sqrt{5}[/tex] + 5 ← collect like terms
= 11 + 5[tex]\sqrt{5}[/tex] ← in the form a + b[tex]\sqrt{5}[/tex]
with a = 11 and b = 5
