Finding cube root by estimation

Let’s do this by examples

Find cube root of 857375.

Step 1:

Make group of 3 digit, starting from right

Step 2:

The unit digit of cube root will be

Unit digit of cube root of 857375 = Unit digit of cube root of 375.

Since 375 ends in 5, it’s cube root will end in 5.

(As 5 ³  = 12 5 , 1 5 ³ = 337 5 )

∴ Unit digit of cube root = 5

Step 3:

Now, for second group.

  8 5 7

We note that

  9 ³ = 729

    & 10 ³ = 1000

So,

    729  < 857 < 1000

       9 ³ < 857 < 10 ³

∴ We take smaller number

So, 9

We put 9 in ten’s place of cube root

Find cube root of 658503.

Step 1:

Make group of 3 digit, starting from right

Step 2 :

The unit digit of cube root will be

Unit digit of cube root of 658503 = Unit digit of cube root of 503

Since 503 ends in 3, it’s cube root will end in 7.

(As 7 ³  = 34 3 , 1 7 ³  = 491 3 )

∴ Unit digit of cube root = 7

Step 3:

Now, for second group.

  6 5 8

We note that

      8 ³ = 512

  & 9 ³ = 729

So,

    512  < 658 < 729

       8 ³ < 658 < 9 ³

∴ We take smaller number

So, 8

We put 8 in ten’s place of cube root.

∴ Cube root of 658503 = 87