Kaplan Nursing Entrance Practice Exam

What is the simplified form of the square root of 108?

1. 3√3

2. 6√3

3. 2√27

4. 3√12

The correct answer is: 6√3

To simplify the square root of 108, start by factoring 108 into its prime factors. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, or more compactly, \(2^2 \times 3^3\). When simplifying a square root, we can take out pairs of prime factors. For every pair of identical factors, one of those factors can be taken out of the square root. 1. From \(2^2\), we can take out one 2 and write this as \(2\). 2. From \(3^3\), we have one complete pair of 3s (which means we can take out one 3), and one remaining 3. Thus, from \(3^3\), we take out one 3 and have \(3^{3-2} = 3\) left inside. Putting it all together: \(\sqrt{108} = \sqrt{2^2 \times 3^3} = 2 \times 3 \times \sqrt{3} = 6\sqrt{3}\). This results in the simplified form of \( \sqrt{108} \) being