\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?

Official Solution:

\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?\)

A. 1
B. 1.7
C. 2
D. 2.4
E. 3

First, let's simplify the expression: \(\sqrt{7 + \sqrt{48}} - \sqrt{3} = \sqrt{7 + \sqrt{16*3}} - \sqrt{3} = \sqrt{7 + 4\sqrt{3}} - \sqrt{3}\). Observe that the answer choices are all rational numbers, so irrational parts in the expression must somehow cancel each other out. This observation should be a hint that we might be able to rewrite \(7 + 4\sqrt{3}\) in a way that makes it the square of something, which would allow us to extract the square root and simplify the expression. Bearing this hint in mind, we rewrite the expression as \(4 + 4\sqrt{3} + 3\). Upon examining the expression \(4 + 4\sqrt{3} + 3\), we notice that \(4 + 4\sqrt{3} + 3 = (2 + \sqrt{3})^2\).

Therefore:

Answer: C­