8
QuizMultiple Choice

Radical Equations — Quiz

Question 8 • Algebra II

Solve the radical equation. square root of 6 n minus 11 end root is equal to n minus 3 Which solution is extraneous?

Answer
A
7
B
There are no extraneous solutions to the equation.
C
10
D
2

Explanation

Squaring both sides gives 6n − 11 = (n − 3)², so n² − 12n + 20 = 0. Factoring gives (n − 2)(n − 10) = 0, so the candidates are 2 and 10. Since the square root is nonnegative, n − 3 must also be nonnegative; n = 2 does not satisfy that condition and fails in the original equation. Therefore, 2 is the extraneous solution, choice D.

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