Simplifying square roots

To simplify a square root:

• Start with finding the prime factorization of the number. If a factor doesn’t have a pair, retain them under the square root symbol, otherwise take the number out.

e.g. $\sqrt{12}=\sqrt{2\ast 2\ast 3}=2\sqrt{3}$

For fractions, $\sqrt{x}\sqrt{y}=\sqrt{\frac{x}{y}}$

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Related

methods for finding the square root of a number

References