Question

Simplify



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

Answer 1

To simplify the expression \((\sqrt{3} + 2)^2\), we can use the formula for the square of a binomial, which states that:

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

In this case, let \(a = \sqrt{3}\) and \(b = 2\). Now we can apply the formula:

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

Calculating each term individually:

1. \((\sqrt{3})^2 = 3\)
2. \(2 \cdot \sqrt{3} \cdot 2 = 4\sqrt{3}\)
3. \((2)^2 = 4\)

Now, combine all the terms together:

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

Finally, combine the constant terms:

\[
3 + 4 = 7
\]

So, we have:

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

Thus, the simplified expression is:

\[
\boxed{7 + 4\sqrt{3}}
\]