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The cube root of 512 is ________.
- a)8
- b)32
- c)16
- d)2
Correct answer is option 'A'. Can you explain this answer?
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The cube root of 512 is ________.a)8 b)32c)16 d)2C...
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The cube root of 512 is ________.a)8 b)32c)16 d)2C...
The cube root of 512 is 8.
To find the cube root of a number, we need to find a number that, when multiplied by itself three times, gives the original number. In this case, we need to find a number that, when multiplied by itself three times, gives us 512.
Prime Factorization of 512:
To solve this problem, we can start by finding the prime factorization of 512. Prime factorization involves breaking down a number into its prime factors.
512 can be written as a product of prime numbers: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^9
Using Prime Factors to Find the Cube Root:
To find the cube root of 512 using prime factors, we need to group the factors in threes. Since 512 has a prime factorization of 2^9, we can group the factors as follows:
(2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2) = (2^3) * (2^3) * (2^3)
Product of Prime Factors:
Now, we can simplify the expression by multiplying the prime factors:
(2^3) * (2^3) * (2^3) = 2^(3+3+3) = 2^9 = 512
Cube Root:
Since (2^3) * (2^3) * (2^3) = 512, we can conclude that the cube root of 512 is 2^3, which simplifies to 8.
Therefore, the correct answer is option 'A', 8.
To find the cube root of a number, we need to find a number that, when multiplied by itself three times, gives the original number. In this case, we need to find a number that, when multiplied by itself three times, gives us 512.
Prime Factorization of 512:
To solve this problem, we can start by finding the prime factorization of 512. Prime factorization involves breaking down a number into its prime factors.
512 can be written as a product of prime numbers: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^9
Using Prime Factors to Find the Cube Root:
To find the cube root of 512 using prime factors, we need to group the factors in threes. Since 512 has a prime factorization of 2^9, we can group the factors as follows:
(2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2) = (2^3) * (2^3) * (2^3)
Product of Prime Factors:
Now, we can simplify the expression by multiplying the prime factors:
(2^3) * (2^3) * (2^3) = 2^(3+3+3) = 2^9 = 512
Cube Root:
Since (2^3) * (2^3) * (2^3) = 512, we can conclude that the cube root of 512 is 2^3, which simplifies to 8.
Therefore, the correct answer is option 'A', 8.
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The cube root of 512 is ________.a)8 b)32c)16 d)2Correct answer is option 'A'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The cube root of 512 is ________.a)8 b)32c)16 d)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cube root of 512 is ________.a)8 b)32c)16 d)2Correct answer is option 'A'. Can you explain this answer?.
The cube root of 512 is ________.a)8 b)32c)16 d)2Correct answer is option 'A'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The cube root of 512 is ________.a)8 b)32c)16 d)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cube root of 512 is ________.a)8 b)32c)16 d)2Correct answer is option 'A'. Can you explain this answer?.
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