Simplify the radical: sqrt(18).

• A. sqrt(18)
• B. 2*sqrt(3)
• C. 3*sqrt(2)
• D. 6*sqrt(2)

Answer: (C)

The idea is to simplify a radical by pulling out any perfect square factors from inside the radical.

18 can be written as 9 × 2, and 9 is a perfect square. So sqrt(18) = sqrt(9 × 2) = sqrt(9) × sqrt(2) = 3 × sqrt(2) = 3√2. This is the simplest radical form because no square factor remains inside the radical.

If you try forms like 2√3 or 6√2, they come from different numbers under the radical (sqrt(12) and sqrt(72), respectively), so they’re not equal to sqrt(18).