Question
The largest four-digit number, which is a perfect cube, is:
- 7000
- 8000
- 9261
- 9999
Hint:
Perfect cube is a number obtained by multiplying the same number thrice by itself.
The correct answer is: 9261
TO FIND-
Largest four-digit number which is a perfect cube.
SOLUTION-
We factorize the given options and check whether it is a perfect cube or not-
a. 7000
7,000 = 10 * 10 * 10 * 7 = 103 * 7
Hence, 7,000 is not a perfect cube as it cannot be written as a number multiplied by itself 3 times.
b. 9999
9,999 = 32 * 11* 101
Hence, 9,999 is not a perfect cube as it cannot be written as a number multiplied by itself 3 times.
c. 8000
8,000 = 20 * 20 * 20
Hence, 8,000 is a perfect cube as it can be written as a number (20) multiplied by itself 3 times.
d. 9261
9,261 = 21 * 21 * 21
Hence, 9,261 is a perfect cube as it can be written as a number (21) multiplied by itself 3 times.
From the above calculations, we observe that- 9261 > 8000
Hence, the largest four-digit number, which is a perfect cube from the given options, is 9261
FINAL ANSWER-
Option 'd' i.e. '9261' is the correct answer to the given question.
Related Questions to study
The least number that should be multiplied with 1008 to make it a perfect square is
Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
FINAL ANSWER REMAINS THE SAME.
The least number that should be multiplied with 1008 to make it a perfect square is
Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
FINAL ANSWER REMAINS THE SAME.
. Round your answer to the nearest whole number.
is between which two integers?
