Teaching Notes 8.18: Solving Radical Equations
To solve radical equations, which are equations that contain a variable in the radicand, students
must follow the same steps as they would to solve multistep equations but with one additional
step. They must square both sides of an equation to eliminate the radical symbol. A common
mistake is to ignore the radical symbol when trying to solve the equation. Another common
mistake is not to substitute their answer inthe original equation to check it.- Explain that a radical equation is an equation that has a variable in the radicand.
- Provide the following example:
√
x=5. Ask your students what they thinkxequals. Most
will quickly tell you the answer is 25. Ask how they arrived at this answer. They might say
that they know 5^2 =25. This concept will help them make the connection between squaring
a number and its square root.- Review the information and examples on the worksheet with your students. Emphasize that
squaring both sides of an equation may produce a solution that is not a solution to the orig-
inal equation. Note that in the second example, the radical is isolated and it is equal to a
negative number. Therefore, there is no real solution. Explain that if students were to con-
tinue and solve forx, and then substitute their answer into the original equation, their
answer would not check.
EXTRA HELP:
If you square a radical, the product is equal to the radicand.ANSWER KEY:
(1)x= 9 (2)x= 16 (3)No real solution (4)x= 618
(5)x= 33 (6)x= 27 (7)x= 32 (8)x= 33
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(Challenge)Jimmy is incorrect. He has to look at the entire equation. If he divides both sides
by−1 to isolate the radical,√
x+ 2 =4, the solution isx=14.
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