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Square Root

A square root of a number is a number that, when multiplied by itself, equals For example, and are the square roots of
All positive numbers have two square roots — one positive and one negative. To avoid ambiguity, when talking about the square root of a number, only the positive root, also known as its principal root, is considered. Furthermore, to denote the square root, the symbol is used. For example, the square root of is denoted as
In the example above, the principal root of is because multiplied by itself equals and is positive. When a number is a perfect square, its square roots are integers. The square roots of positive integers that are non-perfect squares are irrational numbers.
Principal Root of Perfect Squares Principal Root of Non-Perfect Squares
Perfect Square Principal Root
(Integer Number)
Non-Perfect Square Principal Root
(Irrational Number)
The square root of a negative number is not a real number. This is because there is no real number that, when multiplied by itself, results in a negative number.
Instead, the square roots of negative numbers are imaginary numbers.


Square Roots of Fractions and Decimal Numbers
Separate from whole numbers, the square roots of fractions can be calculated by taking square roots of the numerator and denominator separately. Consider the following example.
The square roots of decimal numbers can be calculated by writing them in the fraction form. Then, the square roots of the numerator and denominator are calculated. Consider the following example.