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Square Roots

Elementary

Definition

A number that, when squared, gives the original number.

√a = b \iff b² = a (b ≥ 0)

Definition of square root

√ab = √a · √b

Product rule for square roots

√(a)/(b) = \frac√a√b

Quotient rule for square roots

√a² = |a|

Square root of a square

Example 1

Simplify √50.

√50 = √25 × 2 = 5√2

Example 2

Simplify √12 + √27.

√12 + √27 = 2√3 + 3√3 = 5√3

Pythagorean theorem calculations

Distance, velocity calculations