Question

which of the following numbers are perfect cube

prime factorization method of
512​

Answer 1

Answer:

yes, 512 is a perfect cube of 8

Answer 2

Answer:

Cube root of a number is the number that

multiplies by itself three times to produce the first number. For example, the cube root of 8 is 2

because 2 x 2 x 2 is equal to 8.

We can find the cube root of a number by using the prime factorization method.

In this method, we start dividing the number by the first prime number and continue dividing by 2 until we get a remainder. Then we proceed with the next prime number 3 and so on. Then, we represent the number as the product of prime numbers so obtained. Then, we form triplets by grouping together three of the same factors and write only one from each triplet. We finally multiply the resulting factors to obtain the cube root. Now, let us use the prime factorization method to write 512 as the product of prime numbers.

2/ 512

2 /256

2 /128

2/ 64

2/ 32

2 /16

2 /8

2 /4

2 /2

1 Hence, we have:

512= 2 x 2x2x2x2x2x2x2x2

We now form triplets as follows:

512= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Next, we just take one among each triplet and multiply to get the cube root.

2x2x2 = 8

Hence, the cube root of 512 is 8.