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# 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.

## Video Lesson on Finding Cube Roots 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