Finding the cube roots

Finding Cube Roots requires some background

Background	Last digit
13 =	1	1
23 =	8	8
33 =	27	7
43 =	64	4
53 =	125	5
63 =	216	6
73 =	343	3
83 =	512	2
93 =	729	9

From the above illustration we can take out that last digit of 2³ is 8, 3³ is 7 and vice-versa. All other repeats itself.

Procedure of finding a cube: -

• Start from right and put a comma when three digits are over

Examples: -

9,261

1,728

32,768

175,616

• After putting the comma see the last digit of the number; compare that with table provided above. You get the last digit.
• Now see the first group of numbers and ascertain cube of which number is less than the group. That number is your first digit.
• You have thus found first digit and last digit.

Let us take an example: -

Steps: -

• Counting from last we put comma after 9.
• By seeing the last digit we ascertain that last digit of cube root will be 1.
• Now we see 9 and ascertain that 2³ = 8, is less than 9 and 3³ = 27 is more.
• Our first digit thus comes to 2, and the answer is 21.

Another Example: -

• By seeing last digit we find last digit of cube root is equal to 2.
• By seeing 32 we put 3, as our first digit as 3³ = 27 is less than 32 and 4³ = 64 is more.
• Our answer is 32.