What is the smallest number by which 128 must be multiplied to get a perfect cube?

Class 8Cubes and Cube RootsCubes and Roots

Step-by-Step Solution

128 =

2^{7}

. The next power that is a perfect cube is

2^{9} = (2^{3})^{3}

. To go from

2^{7}

2^{9}

we multiply by

2^{2} = 4

, giving

512 = 8^{3}

Answer: C) 4

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.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Cubes and Cube Roots practice questions

More Class 8 Cubes and Cube Roots practice

What is the smallest number by which 135 must be multiplied to get a perfect cube?What is the smallest number by which 81 must be divided to get a perfect cube?Assertion (A): 3√-64 = −4. Reason (R): The cube root of a negative number is negative.…Express 64 as the sum of consecutive odd numbers that is used in the pattern n³ (for n =…Find the smallest number by which 1000 must be divided to make the quotient a perfect…