- A23
- B50
- C25
- D27
Step-by-Step Solution
135 = . The 5 is unpaired; to make we need two more 5s, i.e. multiply by . Then .
Answer: C) 25
What is the smallest number by which 135 must be multiplied to get a perfect cube?
Class 8Cubes and Cube RootsCubes and Roots
Key idea: Estimating cube roots
For non-perfect cubes, bracket the cube root between two consecutive integers.
Example: ∛100. We know and . 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.
Example: ∛100. We know and . 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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