Question

Which of the following radical expressions has an absolute value symbol in its simplified form?
a. /16x2
b. 3/27x3
c. 5/-32x5
d.3/27x

Answer 1

Answer: a.

Work:
- a. √(16x^2) = 4√(x^2) = 4|x| (even root of x^2 gives |x|)
- b. ∛(27x^3) = 3∛(x^3) = 3x (odd root, no absolute)
- c. ⁵√(-32x^5) = ⁵√(-32)·⁵√(x^5) = -2x (odd root, no absolute)
- d. ∛(27x) = 3∛x (odd root, no absolute)

Only (a) requires an absolute-value sign.