Name Date
WORKSHEET 8.18: SOLVING RADICAL EQUATIONS
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Follow the steps below to solve radical equations:
- Isolate the radical.
- Square both sides of the equation. This will eliminate the radical symbol.
- Solve.
- Check the solution by substituting the value in the original equation.
EXAMPLES
Solve.
√
x+ 3 = 5
√
√^2 x+^4 =−^2
x= 2
√
2 x=− 6 The square root of any number must be≥0.
(
√
x)^2 = 22 There is no real solution.
x= 4
Check:
√
4 + 3 = 5
2 + 3 = 5
DIRECTIONS: Solve each equation.
√
x+ 5 = 8 2.
√
x− 4 = 0
- 2
√
x+ 10 = 6 4.
√
x+ 7 − 4 = 21
- 4 −
√
x+ 3 =− 2 6.
√
2 x− 5 = 7
- 10 +
√
3 x+ 4 = 20 8. 15 −
√
3 x+ 1 = 5
CHALLENGE:Jimmy looked at the equation−
√
x+ 2 =−4. He said that there
is no real solution because the radical equals−4 and square roots are
always positive. Do you agree? Explain your reasoning.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.