Question

Find the cube root of 32768 without prime factorization

Answer 1

Answer:32

Step-by-step explanation:

Prime factors of 32768,

32768 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2

As it is a cube root.....divide the no. Of 2s by 3......the ans is 5.....write 5 times 2..multiply it...

2*2*2*2*2

=32

Answer 2

Given : 32,768

To Find : without factorisation estimate the cube root of 32,768

Solution:

3³  = 27

4³ = 64

30³ = 27000

40³ = 64000

27000 < 32768  < 64000

Taking cube root

30 < ∛ 32768  <  40

Hence cube root lies between 30 and 40

Now  Unit Digit    and  Unit digit of cube

              0                          0

               1                           1

               2                         8

               3                          7

               4                           4

               5                          5

              6                           6

               7                          3

               8                         2

               9                          9

32768 has unit digit 8

Hence ∛ 32768  should have unit digit 2  

So ∛ 32768 =  32

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