Question

find the value of 64 cubed

Answer 1

Answer:

Cube root of 64, 3√64 = 4

mark as brainliest

Answer 2

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