Question

find the cube root of 512 by prime factorization

Answer 1

Answer:

The number 512 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. On combining the prime factors in groups of 3 gives 8. So, the cube root of 512 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 8 (perfect cube).

Step-by-step explanation:

Step :1  The prime factorization of 512 is Factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512. 3√512=3√8×8×8=8. 512 3 = 8 × 8 × 8 3 = 8.

Square Root of 512

In decimal form: ±22.6274.

In radical form: ±16√2.

Step : 2  As a result of 54's prime factorization, which is 2 3 3 3, its lowest radical form, 54's cube root, is written as 3 2. The prime factorization method is a fairly straightforward way to find a number's cube root. The symbol "" designates the cube root. For instance, 8 Equals (2 + 2 + 2) = 2. Finding the cube root of a number is simple since 8 is a perfect cube number.

Step : 3 The concept of a factor rainbow is lovely and ought to be included in every child's mathematical language. The factor rainbow for 6 is as follows: The following integers divide into 6 exactly: 1, 2, 3, and 6. These are the factors of 6. They are arranged in the rainbow in accordance with size, and a bow connects each to its companion.

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Answer 2

The cube root of 512 is 8.

• The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element.
• There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.
• The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are  called factors. A factor is therefore another number's divisor.

Here, according to the given information, we are given that,

The number is 512.

Now, the prime factorization of 512 is,

512 = $2. 2 . 2 .2 . 2 .2 . 2 . 2 . 2$ = $(2. 2 . 2) .(2 . 2 .2 ).( 2 . 2 . 2) = (2^{3} )^{3}$

Then, the cube root of 512 is $2^{3} = 8.$

Hence, the cube root of 512 is 8.

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