Solving cube roots

We will solve the cube roots in two parts. First, we shall solve the right hand part of the answer. If you wish you can solve the left hand part before the right hand part. There is no restriction on either method but generally people prefer to solve the right hand part first.

Steps: -

(Q) Find the cube root of 287496

•   We shall represent the number 287496 as 287|496
  
•   Next, we observe that the cube 287496 ends with a 6 and we know that when cube ends with 6, then the cube root will also ends with 6. Thus our answer at this stage is ____6. We have thus got the right hand part of our answer.
  
•   To find the left hand part of the answer we take the number which lies to the left of the slash. In this case, the number lying to the left hand of the slash is 287. Now, we need to find two perfect cubes between which the number 287 lies in the number line. From the key, we find that 287 lies between the perfect cubes 216 (cube of 6) and 343 (cube of 7).
  
•   Now, find out the numbers obtained above, we take the smaller number and put it on the left hand part of the answer. Thus, out of 6 and 7, we take the smaller number 6 and put it beside the answer is 66. Thus, 66 is the cube root of 287496
  

Examples: -

(Q) Find the cube root of 1404928

•   We shall represent the number 1404928 as 1404|928
  
•   Next, we observe that the cube 1404928 ends with 8 and we know that when cube ends with 2 (2 is the smallest multiple of 8), then the cube root will also ends with 2. Thus our answer at this stage is ____2. We have thus got the right hand part of our answer.
  
•   1404928 lie between 1331 (the cube of 11) and 1728 (the cube of 12). Out of 11 and 12 the smaller number is 11 which we will put beside the 2 already obtained. Hence, the final answer is 112.
  

(Q) Find the cube root of 1557625

•   We shall represent the number 1557625 as 1557|625
  
•   Next, we observe that the cube 1557625 ends with a 5 and we know that when cube ends with 5, then the cube root will also ends with 5. Thus our answer at this stage is ____5. We have thus got the right hand part of our answer.
  
•   We take the number to the left of the slash, which is 1557. In the number line it lies between 100 (the cube of 10) and 1331 (the cube of 11)
  
•   Out of 10 and 11, we take the smaller number 10 and put it beside the 5 already obtained. Our final answer is 105.