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Simplify the following surds. 1. sqrt(12) =

September 28, 2026Mathematics

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Answer

2\sqrt{3}

5 steps

To simplify $\sqrt{12}$ , we need to find the largest perfect square factor of 12.

Find the factors of 12.
The factors of 12 are 1, 2, 3, 4, 6, 12.
Identify the largest perfect square factor.
The perfect square factors of 12 are 1 and 4. The largest is 4.
Rewrite the expression using the perfect square factor.
$\sqrt{12} = \sqrt{4 \times 3}$
Apply the property $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ .
$\sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3}$
Simplify the perfect square root.
$\sqrt{4} \times \sqrt{3} = 2 \times \sqrt{3}$ $= 2\sqrt{3}$
The simplified form of $\sqrt{12}$ is:
$2\sqrt{3}$

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