6
QuizMultiple Choice

Solving Equations Containing Two Radicals — Quiz

Question 6 • Algebra II

Which equation shows a valid, practical step in solving 4th root of 2 x minus 8 plus 4th root of 2 x plus 8 is equal to 0 ?

Answer
A
open paren 4th root of 2 x minus 8 close paren cubed is equal to open paren negative 4th root of 2 x plus 8 close paren cubed
B
open paren 4th root of 2 x minus 8 close paren to the 4th power is equal to open paren negative 4th root of 2 x plus 8 close paren to the 4th power
C
open paren 4th root of 2 x minus 8 close paren cubed is equal to negative open paren 4th root of 2 x plus 8 close paren cubed
D
open paren 4th root of 2 x minus 8 close paren to the 4th power is equal to negative open paren 4th root of 2 x plus 8 close paren to the 4th power

Explanation

First isolate one radical: the fourth root of 2x − 8 equals the negative of the fourth root of 2x + 8. Raising both sides to the fourth power gives choice B. The negative sign is included inside the parentheses, and taking the fourth power removes it because an even power of a negative number is positive.

AI-written and checked against the verified answer.

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