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How many zeros will be there in the cube root of 800?
- a)3
- b)0
- c)1
- d)cube root does not exist
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
How many zeros will be there in the cube root of 800?a)3b)0c)1d)cube r...
To find the cube root of 800, we first need to understand what a cube root is. The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
Now, let's break down the number 800 into its prime factors:
- 800 can be factored as 8 × 100.
- Further breaking it down, 8 is 23 and 100 is 10 × 10, which is 22 × 52.
- So, 800 = 23 × (22 × 52) = 25 × 52.
When we take the cube root, we divide the powers by 3:
- The cube root of 25 is 21.67 (approximately).
- The cube root of 52 is 50.67 (approximately).
After calculating the cube root, we find that 800 does not have any complete sets of three in its prime factorisation. Therefore, it does not produce a whole number.
Thus, the number of zeros in the cube root of 800 is 0.
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How many zeros will be there in the cube root of 800?a)3b)0c)1d)cube r...
Understanding the Cube Root of 800
To determine how many zeros are in the cube root of 800, we first need to calculate the cube root itself.
Step 1: Calculate the Cube Root
- The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- In simpler terms, cube root of "x" is a number "y" such that y * y * y = x.
Step 2: Find the Cube Root of 800
- The prime factorization of 800 is: 800 = 2^5 * 5^2.
- To find the cube root, we can express it as: cube root of (2^5 * 5^2).
- This can be simplified, but we are particularly interested in the decimal or whole number result.
Step 3: Decimal Value of Cube Root
- The cube root of 800 is approximately 9.28.
- This value does not have any zeros in it when written in decimal form.
Conclusion: Number of Zeros
- Since the cube root of 800 is approximately 9.28, it clearly has 0 zeros in its decimal representation.
Thus, the correct answer is option 'B': 0 zeros.
To determine how many zeros are in the cube root of 800, we first need to calculate the cube root itself.
Step 1: Calculate the Cube Root
- The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- In simpler terms, cube root of "x" is a number "y" such that y * y * y = x.
Step 2: Find the Cube Root of 800
- The prime factorization of 800 is: 800 = 2^5 * 5^2.
- To find the cube root, we can express it as: cube root of (2^5 * 5^2).
- This can be simplified, but we are particularly interested in the decimal or whole number result.
Step 3: Decimal Value of Cube Root
- The cube root of 800 is approximately 9.28.
- This value does not have any zeros in it when written in decimal form.
Conclusion: Number of Zeros
- Since the cube root of 800 is approximately 9.28, it clearly has 0 zeros in its decimal representation.
Thus, the correct answer is option 'B': 0 zeros.
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