Teaching Notes 7.5: Adding and Subtracting Radicals
Only radicals with like radicands can be added or subtracted. A common mistake students make is
to add or subtract all radicands.- Explain that to add or subtract radicals, the radicands (the numbers under the square root
symbol) must be the same. - Ask your students to add and simplify
√
9 +
√
- The correct answer is 3+ 4 =7. Compare
this with the common error of adding
√
9 +
√
16 with a result of√
25 =5.
- Now ask your students to subtract and simplify
√
100 −
√
- The correct answer is 10− 8 =
- Compare this with the common error of subtracting
√
100 −
√
64 with a result of√
36 =6.
- Review the information and examples on theworksheet with your students. Sometimes stu-
dents look only at the radicand and assume that because the radicands vary, the radicals can-
not be added or subtracted. Encourage your students to simplify the radicals (if possible) and
then determine if the radicals may be added or subtracted. Note that if there is no number in
front of the radical sign, the number is assumed to be 1. For example,
√
7 +
√
7 = 2
√
- Also
note that not all radicals can be added or subtracted, even when the radical is simplified.
EXTRA HELP:
Although all radicands can be multiplied, only like radicands can be added or subtracted.ANSWER KEY:
(1)−√
10 (2) 2
√
2 + 2
√
5 (3) 4 − 6
√
2 (4)
√
5 +
√
10 (5) 13
------------------------------------------------------------------------------------------
(6)
√
15 − 3
√
10 (7) 5
√
7 (8) 2
√
3 −
√
10 (9)
√
15 + 2
√
5 (10)− 13
√
3
------------------------------------------------------------------------------------------
(11)− 6
√
2 − 10
√
10 (12)
√
5
------------------------------------------------------------------------------------------
(Challenge)Agree. Explanations may vary. A possible explanation is 2+ 2 =4.
------------------------------------------------------------------------------------------260 THE ALGEBRA TEACHER’S GUIDE