Question

Find the square root of 390625 by division method?

Answer 1

Hint: Here in this question we have to determine the square root of the given number, and they have mentioned that we have to determine the square root of a number by the division method. The division method is a specified method and hence we obtain the required solution for the given solution.

Complete step-by-step answer:
The division method is generally explained as
1. Group the digits in pairs, starting with the digit in the units place. ...
2. Find the largest number whose square is equal to or just less than the first period. ...
3. Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder.
Now consider the given number 390625

	625
6+6	390625-36
122+2	306-244
1245	6225-6225
	0

Now we will consider the first two terms of 390625 that is 39, so we divide the number 39 by 6, when 6 is multiplied by 6 we get 36, therefore on subtracting 36 from 39 then the remainder will be 3. Now we take another two digits from the number 390625, so now we will have 306, this number is divided by the number 122, because when we add the number 6 twice we get 12, for the unit place we will consider the number which multiples is near to 306, therefore when 122 is multiplied by 2 we have 244, on subtracting the number 244 from 306 then the remainder will be 62, Now we will take next two digits so now we have 6225, now we are going to divide the number 6225 by 1245 because when we add the number 122 and 2 we get 124, for the unit place we will consider the number which multiples is near to 6225, therefore when 1245 is multiplied by 5 we have 6225, on subtracting the number 6225 from 6225 then the remainder will be 0
Therefore the square root of 390625 is 625

Note: Here in this question we should not get confused by the division method, because to determine the square root by using the division method is totally different, here we will not divide the number not only by one number. So students should not get confused.