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How many zeros will be there in the cube root of 27000?
- a)3
- b)0
- c)1
- d)2
Correct answer is option 'C'. Can you explain this answer??
How many zeros will be there in the cube root of 27000?
a)
3
b)
0
c)
1
d)
2
 | Nishtha Patel answered |
Understanding the Problem
To determine how many zeros are in the cube root of 27000, we first need to calculate the cube root.
Finding the Cube Root of 27000
- The cube root of a number x is a value y such that y^3 = x.
- So, we need to find y such that y^3 = 27000.
Calculating the Cube Root
- We can express 27000 as a power of its prime factors.
- The prime factorization of 27000 is:
- 27000 = 27 x 1000
- 27 = 3^3 and 1000 = 10^3 = (2 x 5)^3
- Therefore, 27000 = 3^3 x (2 x 5)^3 = (3 x 2 x 5)^3 = (30)^3.
- Thus, the cube root of 27000 is:
- Cube root of 27000 = 30.
Counting the Zeros in 30
- The number 30 has one zero when considering the digit representation.
- As per the options provided, the correct answer is option 'C', which indicates there is 1 zero in the cube root of 27000.
Conclusion
- The cube root of 27000 is 30.
- Therefore, the number of zeros in 30 is 1.
This detailed breakdown helps clarify the process and confirms that option 'C' is indeed correct.
To determine how many zeros are in the cube root of 27000, we first need to calculate the cube root.
Finding the Cube Root of 27000
- The cube root of a number x is a value y such that y^3 = x.
- So, we need to find y such that y^3 = 27000.
Calculating the Cube Root
- We can express 27000 as a power of its prime factors.
- The prime factorization of 27000 is:
- 27000 = 27 x 1000
- 27 = 3^3 and 1000 = 10^3 = (2 x 5)^3
- Therefore, 27000 = 3^3 x (2 x 5)^3 = (3 x 2 x 5)^3 = (30)^3.
- Thus, the cube root of 27000 is:
- Cube root of 27000 = 30.
Counting the Zeros in 30
- The number 30 has one zero when considering the digit representation.
- As per the options provided, the correct answer is option 'C', which indicates there is 1 zero in the cube root of 27000.
Conclusion
- The cube root of 27000 is 30.
- Therefore, the number of zeros in 30 is 1.
This detailed breakdown helps clarify the process and confirms that option 'C' is indeed correct.
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