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Find the least number which should be added to 500, in order to make the 500, a perfect cube.
- a)128
- b)63
- c)12
- d)229
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Find the least number which should be added to 500, in order to make t...
500 = 2 × 5 × 5 × 5 = 2 × 53
∴ 12 should be added to make the sum, a perfect cube
∴ 12 should be added to make the sum, a perfect cube
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Find the least number which should be added to 500, in order to make t...
To solve this problem, we need to find the least number that should be added to 500 in order to make it a perfect cube.
To begin, we need to understand what a perfect cube is. A perfect cube is a number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it can be expressed as 2^3.
To find the least number that should be added to 500 to make it a perfect cube, we can follow these steps:
1. Determine the cube root of 500. The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 500 is approximately 7.937.
2. Round up the cube root to the nearest whole number. In this case, the cube root of 500 rounded up is 8.
3. Cube the rounded-up value. 8 cubed is equal to 512.
4. Subtract the original number from the cubed value. 512 - 500 = 12.
Therefore, the least number that should be added to 500 in order to make it a perfect cube is 12.
In summary, we determine the cube root of 500, round it up to the nearest whole number, cube that value, and subtract the original number from the cubed value to find the least number that should be added. In this case, the answer is 12, which corresponds to option C.
To begin, we need to understand what a perfect cube is. A perfect cube is a number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it can be expressed as 2^3.
To find the least number that should be added to 500 to make it a perfect cube, we can follow these steps:
1. Determine the cube root of 500. The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 500 is approximately 7.937.
2. Round up the cube root to the nearest whole number. In this case, the cube root of 500 rounded up is 8.
3. Cube the rounded-up value. 8 cubed is equal to 512.
4. Subtract the original number from the cubed value. 512 - 500 = 12.
Therefore, the least number that should be added to 500 in order to make it a perfect cube is 12.
In summary, we determine the cube root of 500, round it up to the nearest whole number, cube that value, and subtract the original number from the cubed value to find the least number that should be added. In this case, the answer is 12, which corresponds to option C.
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