Simplify

Question

left-parenthesis StartRoot 3 EndRoot plus 2 right-parenthesis squared

Answer options with 5 options
A.
7

B.
4 StartRoot 3 EndRoot

C.
4 plus 7 StartRoot 3 EndRoot

D.
7 plus 4 StartRoot 3 EndRoot

E.
11 StartRoot 3 EndRoot

Answer 1

To simplify \((\sqrt{3} + 2)^2\), we can expand it using the formula for the square of a binomial:

\[ (a + b)^2 = a^2 + 2ab + b^2 \]

Here, \(a = \sqrt{3}\) and \(b = 2\).

Now we calculate each part:

1. \(a^2 = (\sqrt{3})^2 = 3\)
2. \(b^2 = 2^2 = 4\)
3. \(2ab = 2(\sqrt{3})(2) = 4\sqrt{3}\)

Putting this all together:

\[ (\sqrt{3} + 2)^2 = a^2 + 2ab + b^2 = 3 + 4\sqrt{3} + 4 \]

Now, combine the constant terms:

\[ 3 + 4 = 7 \]

So, we have:

\[ (\sqrt{3} + 2)^2 = 7 + 4\sqrt{3} \]

Thus, the simplified form is \(7 + 4\sqrt{3}\).

The correct answer is:

D. \(7 + 4\sqrt{3}\)