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Algebra
Name ___________________
Adding/Subtracting Expressions with Radicals
Some of the properties that apply to products and quotients of radicals do not apply when
working with sums or differences of radicals.
49
4 9
 23
or
6
 36
49
4 9
but
23
cannot be done as
5
6
 13
5
In order to add or subtract radical expressions, we must have the same radicands
(numbers under the
).
Ex 1).
1 5 2 5 3 5
Similar to combining like terms: x  2 x  3x
We are adding “square roots of 5” instead of x’s.
Ex 2).
5 7 3 7  2 7
Sometimes we must write each part of the expression in simple radical form first.
9 32  2
2 7  3 63
Ex 3).
2 7 3 97
Ex 4).
2 7  33 7
9 16  2  2
9  4 2 1 2
2 7 9 7
36 2  1 2
 11 7
 35 2
See Back
Assignment
Use the examples on the front to help you with #1-6.
1).
11  4 11 
2).
9 7 7
3).
2 3  12 
4).
50  8 
5).
7 12  5 27  3 
6).
12  6 3  2 6 
Blast from the Past Section!
7).
9).
3(3n  4)  54  6n
Find the slope of the line passing
through (-2,3) and (4,6).
8).
7 2x  5

3
x
10). Write 2 x  3 y  12 in slope
intercept form and identify m and b.
11). A direct variation graph is a line
which always passes through what point?
12). Solve and graph on a number line:
8 x  2  17 x  9
13). Solve the system:
5 x  6 y  8
5x  2 y  4
14). Simplify:
y 0  (3 x 6 y 3 ) 2