Question

. StartRoot StartFraction 2 (2) (3) (3) (a) (a) (a) (a) (a) (a) (a) (a) Over 3 (3) (5) (5) (a) (a) EndFraction EndRoot

B. StartRoot StartFraction 4 a Superscript 6 Baseline Over 25 EndFraction EndRoot

C. StartFraction 5 Over 25 EndFraction StartRoot StartFraction a Superscript 8 Over a squared EndFraction EndRoot

D.StartFraction 6 Over 15 EndFraction a Superscript 4

E. Two-fifths a cubed

Which expressions listed on the left are equivalent to StartRoot StartFraction 36 a Superscript 8 Baseline Over 225 a squared EndFraction EndRoot? Check all that apply. (Assume that a ≠ 0.)

A
B
C
D
E

Answer 1

Simplify the expression:

sqrt(36 a^8 / 225 a^2) = sqrt((4/25) a^6) = (2/5) sqrt(a^6) = (2/5) |a^3|.

A and B match this exactly:
- A is the original inside the root written out, so it equals the same.
- B is sqrt(4 a^6 / 25), which simplifies to (2/5) |a^3|.

C, D, and E are not equivalent for all nonzero a:
- C = (1/5) |a^3|,
- D = (2/5) a^4,
- E = (2/5) a^3 (equals (2/5)|a^3| only when a>0).

Therefore: A and B.