Question

simplify: $8\sqrt{3} + 7\sqrt{12}$
a) $15\sqrt{15}$
b) $22\sqrt{3}$
c) $15\sqrt{3}$
d) $56\sqrt{3}$

Explanation:

Step1: Simplify \(7\sqrt{12}\)

First, factor 12: \(12 = 4\times3\), so \(\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}\). Then \(7\sqrt{12}=7\times2\sqrt{3}=14\sqrt{3}\).

Step2: Add \(8\sqrt{3}\) and \(14\sqrt{3}\)

Since the radicals are the same (\(\sqrt{3}\)), we add the coefficients: \(8 + 14 = 22\). So \(8\sqrt{3}+14\sqrt{3}=22\sqrt{3}\).

Answer:

B. \(22\sqrt{3}\)