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  • 24-11-2020
  • Mathematics
contestada

Expand and reduce (2+√3)^2

Respuesta :

jimrgrant1 jimrgrant1
  • 24-11-2020

Answer:

7 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a

Given

(2 + [tex]\sqrt{3}[/tex] )² = (2 + [tex]\sqrt{3}[/tex] )(2 + [tex]\sqrt{3}[/tex] )

Each term in the second factor is multiplied by each term in the first factor, that is

2(2 + [tex]\sqrt{3}[/tex] ) + [tex]\sqrt{3}[/tex](2 + [tex]\sqrt{3}[/tex] ) ← distribute both parenthesis

= 4 + 2[tex]\sqrt{3}[/tex] + 2[tex]\sqrt{3}[/tex] + 3 ← collect like terms

= 7 + 4[tex]\sqrt{3}[/tex]

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