Final answer:
The smallest positive whole number that 270 needs to be multiplied by to give a cube number is 6.
Step-by-step explanation:
To find the smallest positive whole number that 270 needs to be multiplied by to give a cube number, we can keep multiplying 270 by consecutive whole numbers until we get a cube number. The cube numbers are the result of multiplying a number by itself three times. So we need to find the smallest whole number that, when multiplied by 270, gives us a cube number.
Let's start by multiplying 270 by 2: 270 × 2 = 540. This is not a cube number since 540 is not the result of multiplying a number by itself three times.
Next, we can try multiplying 270 by 3: 270 × 3 = 810. This is also not a cube number.
We keep multiplying 270 by consecutive whole numbers until we find a cube number. 270 × 4 = 1080 is not a cube number, 270 × 5 = 1350 is not a cube number, and so on.
After trying a few more numbers, we find that 270 × 6 = 1620, which is a cube number. Therefore, the smallest positive whole number that 270 needs to be multiplied by to give a cube number is 6.