# Cube Root of 64

## Trigonometry # Cube Root of 64

The cube root of 64, denoted as 3√64, is a value which results in its original number after getting multiplied by itself, three-times. The cube root of a number is basically the root of a natural number which is cubed. It is a reverse method of evaluating the cube of a number. Say, x3 = y, then 3√y = x.

 Cube root of 64, 3√64 = 4

Let us say, ‘m’ is equal to 3√64, then m × m × m = m3 = 64 (as per the definition of the cube). Since 64 is a two-digit number, we can use here prime factorisation method to find its cube root. Let us learn how to calculate it, without using a calculator.

## How to Find Cube Root of 64

Using the prime factorisation method, we can find the factors present in the given number. If the identical factors are present in a pair of three, under the cube root, then we can easily take them out as a single-digit, because the cube of a number will cancel the cube root.

Let us understand it step by step.

Step 1: By prime factorisation of 64, we get;

64 = 2 × 2 × 2 × 2 × 2 × 2

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.

64 = (2 × 2 × 2) × (2 × 2 × 2)

64 = 23 × 23

Using the law of exponent, we get;

64 = 23+3 = 26 [am.an = (a)m+n]

Or

64 = (22)3 [(am)n = amn]

64 = 43

Step 3: Now, we will take the cube root on both sides of the above expression.

3√64 = 3√(43)

So, here the cube root is eliminated by the cube of 4.

Hence, we get the value of cubic root of 64, i.e.,

3√64 = 4

Since 64 is a perfect cube, therefore it is easy to find its cube root, but for imperfect cubes we have to estimate the values. But it sometimes becomes difficult to evaluate.

Below is the table of cubes of 1 to 10 numbers to find the cube root easily.

 Number (n) Cubes (n3) 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000