Question

Simplify the expression. $$\sqrt{3} \cdot \sqrt{12}$$

Short answer

The simplified expression is 6.

Step-by-step solution

Identify the manipulation technique needed

The expression presented can be simplified by applying the multiplication rule of square roots, which states that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} \). Here \(a = 3\) and \(b = 12\).

Apply the multiplication rule

Multiply 3 and 12 under the square root to get \( \sqrt{3 \cdot 12} = \sqrt{36} \).

Simplify the square root

The square root of 36 simplifies to the number 6, because 6 squared \( (6^2 = 36) \) equals 36.