Question

Find the cube root of 59319 by the estimation method?

Answer 1

Hint:Divide the number into two groups, the last three digits in one group and first two digits in the other group then pick the group which has last three digits (here 319) and then select a number from 1 to 9 so that its unit digit of cube will be 9 then taking the other group which has first two digits, now cubing the numbers from 2 and then see which cube of the number is less than or equal to 59.

Complete step-by-step answer:
First of all divide the given number 59319 into two groups.
59$319$
The bold part of the above number i.e. 319 is in group 1 and the underlined part of the number i.e. 59 is in group 2.
We have asked to find the cube root of 59319 so first we are going to find the unit place of the cube root of 59319 as follows:
Take the number 319. Now take the cube of the number from 2 to 9 and see which number on cubing will give 9 as a unit digit.
Cubing of 9 is 9×9×9= 729.
As you can see the unit digit of the cube of 9 is 729 so the unit digit of the cube root of 59319 is 9.
Now, we are going to find the tens place value of the cube root of 59319.
Take the other group of the number 59319 which is 59. Now, take the cube from number 2 onwards and then see the cubing of which number gives 59 or less than 59.
23 = 8, 33 = 27, 43 = 64
59 lies between 33 and 43 so 33 is a number which is less than 59 so the tens place value of the cube root of 59319 is 3.
Hence, the cube root of 59319 is 39.

Note: Now, if a 6 digit number or greater than that is given then how we are going to find the cube root of that number using estimation method.
Divide the number into groups of 3 digits starting from the right of a number; it is not necessary that all the groups contain 3 digits like in this problem one of the groups contains 2 digits also. The point is grouping of a number should be started from the right of the number.
For example, 256465, first group 465 then group 256. This is how grouping should be done.
And after grouping the method is the same as shown above in the solution part.