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← 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.

$a n x \pm b n x = (a \pm b) n x$

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

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,

n x

is a real number. This means that the Distributive Property can be used to factor out

n x .

a n x \pm b n x

FactorOut

Factor out $n x$

(a \pm b) n x

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Proof