The value 5122 is 262,144, because we multiply 512 by itself, which is known as squaring.

When 0 is written as a power or degree of any number, we get 1 always, so 10 is 1.

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Last updated on December 11th, 2024

Cube root of 512

Q: Is 0 a perfect square

Yes, 0 is a perfect square because when we multiply 0 with itself we get zero and any number which is squared in zero gives zero, which makes it a perfect square.

Q: Is, 8000 a perfect cube

Yes, 8000 is a perfect cube as it is equal to 20 × 20 x 20 x 20 or can be written as 203.

Q: What is the value of (2)⁹?

2 multiplied 9 times gives 512, 9 is the power or degree of 2. 29=512.

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We can define a cube root as a number that, when multiplied by itself three times, gives you the original number. The cube of a number is represented as X3 and the cube root of a number is represented as ∛x. Cube roots are used with several applications in our day-to-day lives, such as in the field of Scaling Models and Designs, which helps create miniature models of buildings, aircraft, or cars.

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.

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.