A perfect square-root chart lists the integer roots of numbers that have no fractional component. Multiplying these square roots by themselves results in designated perfect squares. For example, the square root of nine is three. Nine is a perfect square and three is a perfect square root.
Websites and textbooks often publish perfect square-root charts. When looking at a multiplication table, the perfect squares form a diagonal line beginning at zero. Students who are familiar with their multiplication tables have the ability to recognize the perfect squares of the integers from zero to ten and the perfect square roots of numbers zero to 100.
Perfect square roots include both positive and negative integers. Multiplying two negative numbers always produces a positive number. When the square-root symbol or radical is used, this indicates the positive square root. However, the perfect square has another set of roots that are negative.
In algebra, one method of factoring includes completing the square. In this process, mathematicians add the same number to both sides of the equation to create an algebraic perfect square on one side of the equation. Solving the problem becomes a matter of taking the square root of both sides of the equation and remembering the roots are both positive and negative.