Check sibling questions

Let’s do this by examples

Find cube root of 857375.

 

Step 1:

Make group of 3 digit, starting from right

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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

Finding cube root by estimation - Part 2

 

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

Finding cube root by estimation - Part 3

 

Find cube root of 658503.

Step 1:

Make group of 3 digit, starting from right

Finding cube root by estimation - Part 4

 

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

Finding cube root by estimation - Part 5

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.

Finding cube root by estimation - Part 6

∴ Cube root of 658503 = 87

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.