Keyword Analysis & Research: cube root of 512 by prime factorization

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Frequently Asked Questions

What is the cube root of 512?

The cube root of 512 is a value that results in its original number after getting multiplied by itself, three-times. It is denoted as 3 āˆš512. The cube root of a number is basically the root of a number that is cubed. If x 3 = y, then 3 āˆšy = x. Thus, it is a reverse method of finding the cube of a number.

Is 512 a rational number?

As we know, the cube root value is a whole number (cube root of 512 = 8), and we can say that it is a rational number. Why 512 is not a perfect square? 1, 64 and 729 are the only numbers that are both perfect squares and cubes between 1 and 1000.

How to find the cube root of a number?

Thus, it is a reverse method of finding the cube of a number. Say, ā€˜nā€™ is the value obtained from 3 āˆš512, then n × n × n = n 3 = 512 (as per the definition of a cube). Since 512 is a perfect cube, we will use here the prime factorisation method, to get the cube root easily.

How to get cubes of prime factors?

Now when we take the cube root of the given number, the identical or similar factors can be paired in a group of three. Hence, we will get the cubes of prime factors. Now, on applying the cube root it gets cancelled by the cubed number present within it.


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