Cube root of 45 is between what two consecutive integers?

Cube root of 258 is between what two consecutive integers?

start listing the cubes:

1: 1
2: 8
3: 27
...

Then pick the two numbers from column 1 that correspond to the cubes near your targets in column 2.

Or, just find the cube roots of your numbers.

For example, ∛60 = 3.91

so, it is between 3 and 4, since
3^3 = 27
4^3 = 64

To find the cube root of a number, we can use estimation.

1. For the cube root of 45:
- Start by taking the cube root of the perfect cubes around 45. The cube root of 27 is 3, and the cube root of 64 is 4.
- Since 45 is between 27 and 64, the cube root of 45 is between 3 and 4.

Therefore, the cube root of 45 is between 3 and 4.

2. For the cube root of 258:
- Taking the cube root of perfect cubes around 258, the cube root of 216 is 6, and the cube root of 343 is 7.
- Since 258 is between 216 and 343, the cube root of 258 is between 6 and 7.

Therefore, the cube root of 258 is between 6 and 7.

To find the cube root of a number, you can use a calculator or perform an estimation by trying different values until you get close enough to the actual value.

For the first question, to find the cube root of 45, you can start by trying different cube roots of numbers until you narrow it down to a specific range. Let's start by trying some consecutive integers.
Cube root of 2 is approximately 1.26 (1³ = 1),
Cube root of 3 is approximately 1.44 (2³ = 8),
Cube root of 4 is approximately 1.59 (2³ = 27),
Cube root of 5 is approximately 1.71 (2³ = 64),
Cube root of 6 is approximately 1.82 (2³ = 125),
Cube root of 7 is approximately 1.91 (2³ = 216),
Cube root of 8 is approximately 2 (2³ = 343),
Cube root of 9 is approximately 2.08 (2³ = 512),
Cube root of 10 is approximately 2.15 (2³ = 729),
Cube root of 11 is approximately 2.22 (2³ = 1000),
Cube root of 12 is approximately 2.29 (2³ = 1331),

Since the cube of 3 is 27 and the cube of 4 is 64, the cube root of 45 is between 3 and 4.

For the second question, let's perform the same process.
Cube root of 7 is approximately 1.91 (1³ = 1),
Cube root of 8 is approximately 2 (2³ = 8),
Cube root of 9 is approximately 2.08 (2³ = 27),
Cube root of 10 is approximately 2.15 (2³ = 64),
Cube root of 11 is approximately 2.22 (2³ = 125),
Cube root of 12 is approximately 2.29 (2³ = 216),
Cube root of 13 is approximately 2.36 (2³ = 343),
Cube root of 14 is approximately 2.42 (2³ = 512),
Cube root of 15 is approximately 2.48 (2³ = 729),
Cube root of 16 is approximately 2.54 (2³ = 1000),
Cube root of 17 is approximately 2.60 (2³ = 1331),

Since the cube of 6 is 216 and the cube of 7 is 343, the cube root of 258 is between 6 and 7.