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Chapter 8: Problem 1

Simplify. $$\sqrt{12}$$

Short Answer

Expert verified
The simplified form of \(\sqrt{12}\) is \(2\sqrt{3}\).

Step by step solution

01

Factorize

First, factorize 12 into a product of prime numbers: \(12 = 2 * 2 * 3\) or equally \(12 = 2^2 * 3\).
02

Apply Square Root Rules

Apply square root rules and simplify. \(\sqrt{12} = \sqrt{(2^2 * 3)}\). The square root of \(2^2\) can be taken out from under the root as the square root of \(2^2 = 2\). Therefore, \(\sqrt{(2^2 * 3)} = 2\sqrt{3}\).
03

Final Simplified Form

Finally, the simplified form of \(\sqrt{12}\) is \(2\sqrt{3}\).

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