Finding cube root by estimation

Chapter 6 Class 8 Cubes and Cube Roots
Concept wise

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

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