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1600 = . By what least whole number must 1600 be multiplied to give a perfect cube, and what is the cube root of that product?

Class 8Cubes and Cube RootsCubes and Roots
  • A2; cube root 20
  • B5; cube root 40
  • C25; cube root 20
  • D5; cube root 20

Step-by-Step Solution

is already two complete triples, but is one 5 short. Multiply by 5: , whose cube root is 20. Multiplying by 25 overshoots — that would be the fix only if a single 5 were present.
Answer: D) 5; cube root 20

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.

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