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Simplifying square roots

A square root is simplified by taking out the largest square factor under the root sign. The product rule says that the root of a product is the product of the roots, so a square factor becomes an integer in front of the root. You cannot split a sum under the root: $\sqrt{a + b}$ is not $\sqrt{a} + \sqrt{b}$. The same rule applies when you combine like roots.

Symbols

Example

$\sqrt{50} = \sqrt{25\cdot 2} = 5\sqrt{2}$.

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Part of Mathematics 1T: Powers, roots and logarithms.