ACT Preparation / Unit 11 ACT 1010 short lesson, about 20 seconds
Radical Equations and Extraneous Solutions
Captions available
The idea
To solve a radical equation, isolate the radical, raise both sides to the root's index, and solve. Then check every answer in the original equation.
In practice
√(x + 6) = x gives x + 6 = x², so x = 3 or x = −2; only 3 checks.
Where people slip
Squaring can create extraneous solutions that fail the original: √4 is 2, never −2.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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