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Which is the least number which should be added to 1720,in order to make it a perfect cube?
- a)269
- b)8
- c)469
- d)58
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which is the least number which should be added to 1720,in order to ma...
1720 > 1000 = 103
∴ 113 = 1331, 123 = 1728
∴ 1728 – 1720 = 8 should be added to 1720 to make the sum, a perfect cube.
∴ 113 = 1331, 123 = 1728
∴ 1728 – 1720 = 8 should be added to 1720 to make the sum, a perfect cube.
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Which is the least number which should be added to 1720,in order to ma...
Problem Statement: Find the least number that should be added to 1720 to make it a perfect cube.
Solution:
Let us first find the cube root of 1720.
∛1720 = 12.995
We know that the cube of any number ending with 5 will end with 5.
Therefore, let us add a number to 1720 such that it ends with 5.
1720 + x = n^3
The possible numbers that can be added to 1720 such that it ends with 5 are 5, 15, 25, 35, 45, 55, 65, 75, 85, and 95.
Let us substitute these values in the above equation and check which one gives us a perfect cube.
For x = 5, n^3 = 1725, which is not a perfect cube.
For x = 15, n^3 = 1735, which is not a perfect cube.
For x = 25, n^3 = 1745, which is not a perfect cube.
For x = 35, n^3 = 1755, which is not a perfect cube.
For x = 45, n^3 = 1765, which is not a perfect cube.
For x = 55, n^3 = 1775, which is not a perfect cube.
For x = 65, n^3 = 1785, which is not a perfect cube.
For x = 75, n^3 = 1795, which is not a perfect cube.
For x = 85, n^3 = 1805, which is not a perfect cube.
For x = 95, n^3 = 1815, which is not a perfect cube.
Therefore, the least number that should be added to 1720 to make it a perfect cube is 8.
1720 + 8 = 1728, which is a perfect cube of 12.
Hence, option B is the correct answer.
Solution:
Let us first find the cube root of 1720.
∛1720 = 12.995
We know that the cube of any number ending with 5 will end with 5.
Therefore, let us add a number to 1720 such that it ends with 5.
1720 + x = n^3
The possible numbers that can be added to 1720 such that it ends with 5 are 5, 15, 25, 35, 45, 55, 65, 75, 85, and 95.
Let us substitute these values in the above equation and check which one gives us a perfect cube.
For x = 5, n^3 = 1725, which is not a perfect cube.
For x = 15, n^3 = 1735, which is not a perfect cube.
For x = 25, n^3 = 1745, which is not a perfect cube.
For x = 35, n^3 = 1755, which is not a perfect cube.
For x = 45, n^3 = 1765, which is not a perfect cube.
For x = 55, n^3 = 1775, which is not a perfect cube.
For x = 65, n^3 = 1785, which is not a perfect cube.
For x = 75, n^3 = 1795, which is not a perfect cube.
For x = 85, n^3 = 1805, which is not a perfect cube.
For x = 95, n^3 = 1815, which is not a perfect cube.
Therefore, the least number that should be added to 1720 to make it a perfect cube is 8.
1720 + 8 = 1728, which is a perfect cube of 12.
Hence, option B is the correct answer.
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