Introduction to Radicals

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Introduction to Radicals

When simplifying square roots, we give the positive and negative answer if solving an equation that did not originally have a square root. Otherwise, we give only the principal root. Square roots of negative numbers have non-real answers, which is why square roots of variables sometimes include the condition that the variable is greater than zero. Knowledge of math radicals is important when solving quadratic equation problems.
This video introduces radicals and explains how to simplify perfect square, cube, and nth roots.

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Radicals and Absolute Values

Since any even-numbered root must be a positive number (otherwise it is imaginary), absolute value must be used when simplifying roots with variables, which ensures the answer is positive. When working with radical expressions this requirement does not apply to any odd root because odd roots exist for negative numbers. Additionally, absolute value is not needed if an even number of a variable come out of the root - the answer must be positive.
How to know when to include a absolute value when simplifying a square root?

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Principle Square Root
Why do the answers for simplifying radicals in the back of the book have those annoying absolute value bars?

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