Cube root using ones and tens method

Using ones and tens method, we can find the cube root of any perfect cube having at most 6 digits.This method is not applicable for the number having more than 6 digits like 5832000. So,keep it in mind while using this method 

Important points : 

  • If a number ends with digit 0,1,4,5,6 and 9 .Then ,their cube also ends with digit 0,1,4,5,6 and 9 respectively .
  • Whereas, if a number ends with digit 2 or 3 .then, their cube ends with 8 and 7 respectively.

You can see in the given table :

The red box and yellow box indicates the above two conditions respectively 

Cube of number from 1 to 20

Let’s talk about step by step procedure to calculate cube root using the ones and tens method 

Step:01 Find the one’s digit of the required cube root.

Step:02 Cross out the last three-digit of the number 

Step:03 Think of the number whose cube root is less than or equal to the remaining digit of the number (Digit left after Step:02) 

Let’s take a number and try to find its cube root using the ones and tens method . Assumed number: 91125 

Solution: 

Step:01 Find the unit digit of the required cube root 

Since we know 91125 is a perfect cube and its unit digit is 5 . So, its cube root unit digit will also 5.

See above table 

Step:02 Cross out the last three-digit of the number

Cube root of 91125

Step:03 Think of the number whose cube is less than or equal to the remaining digit of the number (Digit left after Step:02)

After crossing out the last 3 digits,we have 91 as the remaining number. Now, think of a number whose cube is less than or equal to 91.

Cube root of 911254³= 64 and 5³=125, 91 lies between cubes of 4 and 5.

So, 4 is the tens digit of the required cube root and we have already found one’s digit in step:01 i.e 5. 

Hence, cube root of 91125 is 45 

 Examples : 

Q.1 Find the cube root of 531441 using the ones and tens method 

Solution: 

Since,

Unit digit of 531441 is 1 . So, 1 will also be the unit digit of the required cube root 

Now  strike out the last three-digit of the 531441 

Cube root of 531441

Remaining number = 531 

Think of the number whose cube is less than or equal to 531.See above table

Cube root of 531441 

531 lies between cubes of 8 and 9 

So, 8 is the tens digit of the cube root and we have found one’s digit i.e 1 

Hence, the cube root of 531441 is 81 

Practice problem 

Q .Find the cube root of following number using ones and tens method 

(i) 4096 

(ii) 110592 

(iii) 389017 

(iv) 592704 

(v) 5832000 

Check your answer

(i) 16 

(ii) 48 

(iii) 73

(iv) 84

(v) Can’t find ,it has more than 6 digits 

Check these stuff as well : 

 

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