# how would you do the cube root of 64 WITHOUT calculator?

math homework, appreciate help!

• Not that 4*4=16 and 16*4=64. So, 4*4*4 = 16*4 = 64. Thus, the cube root of 64 is 4.

• The long form solving of a cube root begins with the knowledge of a few basic cube roots including “64”.

I’m not sure what your teacher is looking for but you could demonstrate a trial and error approach:

Attempt 1: 3*3*3=27

Attempt 2: 5*5*5=125

Attempt 3: 4*4*4=64 Success!

As far as I know, long form cube roots requires a memorized set of the basic cubes of 2,3,4,5,6,7,8 and 9. Getting the cube of 65 for example starts with a knowledge that 4 cubed is 64.

4.

3/———–

/ 65

-64

——-

1.000

The next decimal would be a value of x that would make the next equation less than 1000 for:

(4^2 *300 + 4*30 * X+X^2 ) * X

in this case X = 0

So the solution is tending towards 4.0_ _ _

Eventually, you will get 4.02 using this method. But as you can see, I needed to know off the start that 4 was the cube of 64. This can only be “PROVEN” via the forwards of:

4*4=16

16*4 = 64.

• Cube Root Of 64

• knowing that 64 = 8*8 and that the cube root of 8 = 2, i’d say the cube root of 64 = 2*2 = 4

• You factor it out to primes:

2*2*2*2*2*2 = 64

If you need the square root you would divide it into two sets: (2*2*2)(2*2*2)=8×8=64.

If you need the cube root you just divide it into three sets: (2*2)(2*2)(2*2)=4*4*4=64

The same thing could be done for sixth root.

So four is your answer, just through a few more examples up there.

• after a while you know this from problems you have done. so remember cube root of 64 = 4

4 * 4 * 4 = 64

• Just factorize it and get the answer

64 = 2^6

taking cube root => dividing power by 3

Therefore the answer is 2^2 = 4.

• Look at the prime factorization of 64:

64 = (2 x 2) x (2 x 2) x (2 x 2)

The terms can be associated into three identical groups, hence

CubeRoot(64) = (2 x 2) = 4

• 4 x 4 x 4 = 64