Question

Find the cube root of 2197 numbers using estimation method​

Answer 1

For calculating the cube root of 2197, this number has to be separated in two group, i.e. 2 and 197.

considering the group 197:

197 ends with 7 and we know that if digit 7 is at the end of any perfect cube number, then its cube root will have 3 at its unit place only. Therefore, the digits at the units place of the required cube root is taken as 3.

Now consider the other group 2:

We know that the 13=1 and 23=8 

Also, 1<2<8 

So, 1 will be taken at the tens place. So, the required cube root of 2197 is 13.

3 root over 2197=13

Answer 2

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Step 1:

Take the digit present at the unit’s place of 2197.

Unit Place of 2197 has —> 7

Step 2:

Check with the cubes table provided above. The cube of which number has 7 at its unit place?

Clearly, 33 = 27

That means the cubic root of 2197 will have 3 at the unit place.

Say, 3√2197 = ?3

Step 3:

So, we have got the unit place digit of the required value.

Now ignore the last 3 digits of 2197, i.e. 197

Taking 2 as a reference number, we can see 2 lies between 13 and 23, i.e., between 1 and 8.

So, we will choose here the lowest number, nearest to 2, which is 1.

Since, 13 = 1, therefore, we will have 1 as the first digit of the required number.

☞ Hence, 3√2197 = 13

hope it was helpful to you