Operating with Square Roots
Rule

Adding and Subtracting Radicals

A numeric or algebraic expression that contains two or more radical terms with the same radicand and the same index — called like radical expressions — can be simplified by adding or subtracting the corresponding coefficients.

Here, and are real numbers and is a natural number. If is even, then must be greater than or equal to zero.

Proof

If is an even number, then is greater than or equal to zero. If is odd, then can be any real number. In both cases, is a real number. This means that the Distributive Property can be used to factor out
Exercises
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