Note: Portions of this document are excerpted from the textbook Prealgebra, 7th ed. by Charles
McKeague
Section 5.9 Adding and Subtracting Square Roots
1. Combining Similar Square Roots: We add or subtract square
roots in the same way that we add similar terms. Two square roots can
be added or subtracted if the expressions under the square root are
identical. The addition or subtraction is performed by using the
distributive property.
Example 1: Simplify. Give exact answers.
a. 4 2 +3 2 =4•2+3•2=4+3
( )
2=7 2
b. 5 3 +7 3
c. 7 5 −11 5
d. 21 11 −11
e. 13 +11
2. Adding and Subtracting Square Roots When Simplification is
Required First: If the expressions under the square root are not
identical, then the square roots can’t be added or subtracted. However,
sometimes the square roots can be simplified and then added or
subtracted.
Example 2: Simplify. Give exact answers.
a. 12 +27
