Sign In
Two radicals can be added or subtracted if it is possible to rewrite them as like radical expressions. Use the Distributive Property to add or subtract like radicals.
asqrt(x) + bsqrt(x) = ( a + b) sqrt(x)
asqrt(x) - bsqrt(x) = ( a - b) sqrt(x)
For example, consider the following radical expressions. sqrt(x^5 y^3) and sqrt(16xy^7) In order to add these expressions, there are three steps to follow. Note that subtraction of the radicals can be performed by applying the same three steps, only instead of adding the like radicals, they will be subtracted.
Split into factors
Write as a sum
a^(m+n)=a^m*a^n
Commutative Property of Multiplication
sqrt(a* b)=sqrt(a)*sqrt(b)
a^1=a
sqrt(a^4)=|a|
Write as a power
a^m* b^m=(a * b)^m
sqrt(a^4)=|a|
Multiply
Since both the index and the radicand of the roots are identical, they are like radical expressions.