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415 LearnersLast updated on August 5, 2025
Cube root of 512
What is the cube root of 512?
The cube root of 512 is 8. The cube root of 512 is expressed as ∛512 in radical form, where the ∛ sign is called the radical sign. In exponential form, it is written as (512)⅓
Finding the cube root of 512
We can find the cube root of 512, mainly through two methods:
- Prime Factorization method.
- Subtraction method.
Cube root of 512 by Prime Factorization method
Finding a cube root of 512 through the Prime Factorization method involves determining the factor of 512.
Step 1 — Find the prime factors of 512.
So the prime factor of 512 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Step 2 — Group the factors of 512 in a group of 3.
Step 3–We have 9 digits, which makes a set of 3 triplets.
Note: During Prime factorization, a pair of 2 digits is made in square roots, whereas in a cube a triplet is made.
The cube root of 512 can be written as ∛512 = ∛(2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 2 × 2 × 2 = 8. Therefore, the cube root of 512 is 8.
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Cube root of 512 by Subtraction method
The subtraction method involves subtracting successive numbers repeatedly.
Subtract the numbers 1,7,19,37,61,91,127,169,217,331,397……..successively till we get a zero.
Subtracting the successive number method is based on the properties of cubes and the differences between consecutive cubes. Here, the subtraction took place in 8 steps to reach zero. Hence, the cube root of 512 is 8.
Common Mistakes and How to Avoid Them in the Cube Root of 512
While solving problems on cube roots, children are likely to make common mistakes, here are a few mistakes and how to avoid them.
Mistake 1
Misunderstanding the powers
You can divide 512 by 3, thinking the answer is a part of the process to find out the cube root, so you need to be aware of the relation between exponents and cube roots. This error arises from misunderstanding the relation between exponents and cube roots, assuming that division by 3 is a part of finding the cube root.
Mistake 2
Confusing cube roots with Factorization
You might break down 512 into 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 but forget to combine them into triplets. You need to be aware that after breaking down, the factors need to be in a group of triplets.
Mistake 3
Forgetting the Multiplication of three same numbers
You might multiply 2 × 9 instead of understanding the correct multiplication as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. You should be aware of the basis of solving a cube root. This shows a fundamental gap in understanding the concept of cubing a number, leading to incorrect multiplication steps.
The cube root of 512 examples
Problem 1
Show if 512 is a perfect cube.
Yes, 512 is a perfect cube
Explanation
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Sorting the prime factors in pairs of three gives us 8
2 × 2 × 2 = 8
Thus, 512 is a perfect cube.
Problem 2
What is the value of 7+1∛512
15
Explanation
: Let the number be X
So, X = 7+1 × ∛512
8 is the cube root of 512
X = 7+1 × 8
X = 7+8
X = 15
Problem 3
What is the ∛-512?
-8
Explanation
A negative number always has a negative cube root
FAQs of the 512 cube root
1.Is 0 a perfect square
2.What is (512)²
3.Is, 8000 a perfect cube
4.What is the value of (2)⁹?
5.What is (1)⁰?
Important Glossaries for Cube Root of 512
- Powers: Powers are the degrees of a particular number, which can be used to represent squares/cubes of numbers.
- Perfect Cube: It is the product of a particular number when multiplied by itself.
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