Solved Questions on Cube Roots
1. Find cube root of 857375 by estimation method.
a) 35
b) 55
c) 75
d) 95
Answer: d) 95
Explanation: Make groups of three numbers starting from the right.
By looking at the number 375, we can say that the final digit from the right is 5.
Now take the number in the second group 857.
We know that 93 = 729 and 103 = 1000.
1000 is greater than 857 so we need to consider the smaller number which is 729. Hence, the first number is 9.
Therefore, the cube root of 857375 is 95.
2. Find the cube root of 4096 by estimation method.
a) 15
b) 16
c) 36
d) 66
Answer: b) 16
Explanation: Start with an estimate. A good estimate would be to choose a perfect cube number that is close to 4096. For example, we can start with an estimate of 16, since 163 = 4096.
Cube the estimate to see if it is close to the original number. In this case, 163 = 4096, so the estimate is correct.
If the estimate is not correct, adjust it based on how far off it was. For example, if we wanted to find the cube root of 8000 and our estimate was 20, we would see that 203 = 8000, so our estimate is correct. However, if our estimate was 19, we would see that 193 = 6859, which is too low. To adjust our estimate, we would try a larger number, such as 20, since 203 = 8000, which is too high. Based on these results, we could refine our estimate to be between 19 and 20.
Repeat the steps until we get an estimate that is as close as possible to the actual cube root. In this case, we do not need to repeat the steps as our initial estimate was correct.
Therefore, the cube root of 4096 is 16.
3. Find the cube root of 216 using prime factorization method.
a) 6
b) 16
c) 26
d) 36
Answer: a) 6
Explanation:
4. Find the cube root of 2744 by the division method.
a) 12
b) 14
c) 23
d) 26
Answer: b) 14
Explanation:
Practice Questions on Cube Roots
1. Find the cube root of 64 using prime factorization method.
a) 4
b) 3
c) 2
d) 1
Answer: a) 4
2. Find the cube root of 125 using the estimation method.
a) 35
b) 25
c) 15
d) 5
Answer: d) 5
3. Find the cube root of 238328 by the long division method.
a) 22
b) 42
c) 62
d) 82
Answer: c) 62
4. Find the cube root of 15625 using the estimation method.
a) 15
b) 25
c) 35
d) 45
Answer: b) 25
5. Alen got 46656 points from her teacher, He wants to find the cube root of it using prime factorization method. What is the cube root of it?
a) 16
b) 36
c) 56
d) 66
Answer: b) 36
6. Simplify: ?(125 x 64)
a) 20
b) 15
c) 12
d) 10
Answer: a) 20
7. What is the cube root of 35937?
a) 33
b) 45
c) 27
d) 12
Answer: a) 33
8. What is the cube root of 6859?
a) 27
b) 17
c) 19
d) 39
Answer: c) 19
9. Find the cube root of 1331 using prime factorization method.
a) 11
b) 21
c) 31
d) 41
Answer: a) 11
10. Find the cube root of 941192 using division method.
a) 99
b) 98
c) 78
d) 58
Answer: b) 98
