Test
Irrational equations
This test develops methods for equations containing square and cube roots. Tasks require students to determine the domain, raise both sides to a power and check for extraneous solutions introduced during transformation.
Time left: 00:00:00
Sample questions
- Solve √(x + ___) = ___.
- Solve ___√x + (___) = 0.
- Solve ∛(x³ + ___) = ∛___.
- After squaring an irrational equation, a candidate root is obtained. What should be done?
Irrational equations
In an irrational equation, the unknown occurs under a radical. The radicand of an even root must be non-negative, and an isolated square root cannot equal a negative expression.
The risk of squaring
Isolate one radical and square both sides, repeating if necessary. Raising both sides to an even power is not equivalent without sign restrictions and may create extraneous roots. Every candidate must therefore be substituted directly into the original equation.
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