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.

asqrt(x)± bsqrt(x)=(a± b)sqrt(x)

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

Proof

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

asqrt(x)± bsqrt(x)
(a± b)sqrt(x)

Exercises
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