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

math homework, appreciate help!

15 Answers

  • 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

    Answer is 4

  • factor out 64

    64 = 8(8) = 2(4)(2)(4) = 4(4)(4)

    so, cube root of 64 = cube root of [4(4)(4)] = 4

    hope this helps

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