Question

Expand and reduce (2+√3)^2

Answer 1

Answer:

7 + 4$\sqrt{3}$

Step-by-step explanation:

note that $\sqrt{a}$ × $\sqrt{a}$ = a

Given

(2 + $\sqrt{3}$ )² = (2 + $\sqrt{3}$ )(2 + $\sqrt{3}$ )

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

2(2 + $\sqrt{3}$ ) + $\sqrt{3}$(2 + $\sqrt{3}$ ) ← distribute both parenthesis

= 4 + 2$\sqrt{3}$ + 2$\sqrt{3}$ + 3 ← collect like terms

= 7 + 4$\sqrt{3}$