A perfect cube ends in the digit 2. What is the units digit of its cube root?

Class 8Cubes and Cube RootsCubes and Roots

Step-by-Step Solution

Only 8 cubes to a number ending in 2, since

8^{3} = 512

. So the root must end in 8. Choosing 2 assumes the root ends in the same digit as the cube — that holds for 0, 1, 4, 5, 6 and 9, but 2 and 8 swap places (and so do 3 and 7).

Answer: D) 8

Key idea: Estimating cube roots

For non-perfect cubes, bracket the cube root between two consecutive integers.

Example: ∛100. We know

4^{3} = 64

and

5^{3} = 125

. So 4 < ∛100 < 5. Closer to 5 (100 is closer to 125 than 64). Refined estimate: ∛100 ≈ 4.64.

For perfect cubes, look at the last digit (last digit rule for cubes: each digit cubes to a unique last digit). 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0.

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