Question

Find the square root of the following numbers by division method.
i. 1089
ii. 2304
iii. 7744
iv. 6084
v. 9025

Answer 1

Hint: Before attempting this question one should have prior knowledge about the division method and the steps included in this method, use this information to approach towards the solution of the question.

Complete step-by-step answer:
According to the given information we have 5 numbers of which we have to find the square root by division method
(i) 1089
By the division method
Taking 10 as first pair of digits and 89 as second pair of digits
Now taking 3 as divisor and quotient since square of 3 is smaller than first pair of digits
Bringing the remainder to the left side of the next pair
Now taking 6 as the first part of divisor and 3 as the second part of divisor and quotient is equal to 3 as the product is equal to the new dividend
So the result is

	33
3	\[\overline {10} \]\[\overline {89} \]
+3	9
63	189
	189
	0

Therefore the square root of 1089 is 33
(ii) 2304
By the division method
Taking 23 as first pair of digits and 04 as second pair of digits
Now taking 4 as divisor and quotient since square of 4 is smaller than first pair of digits
Bringing the remainder to the left side of the next pair
Now taking 8 as the first part of divisor and 8 as a second part of divisor and the quotient is equal to 8 as the product is equal to the new dividend
So the result is

	48
4	\[\overline {23} \]\[\overline {04} \]
+4	16
88	704
	704
	0

Therefore the square root of 2304 is 48
(iii) 7744
By the division method
Taking 77 as first pair of digits and 44 as second pair of digits
Now taking 8 as divisor and quotient since square of 8 is smaller than first pair of digits
Bringing the remainder to the left side of the next pair
Now taking 16 as the first part of divisor and 8 as a second part of divisor and the quotient is equal to 8 as the product is equal to the new dividend
So the result is

	88
8	\[\overline {77} \]\[\overline {44} \]
+8	64
168	1344
	1344
	0

Therefore the square root of 7744 is 88
(iv) 6084
By the division method
Taking 60 as first pair of digits and 84 as second pair of digits
Now taking 7 as divisor and quotient since square of 7 is smaller than first pair of digits
Bringing the remainder to the left side of the next pair
Now taking 14 as the first part of divisor and 8 as a second part of divisor and the quotient is equal to 8 as the product is equal to the new dividend
So the result is

	78
7	\[\overline {60} \]\[\overline {84} \]
+7	49
148	1184
	1184
	0

Therefore the square root of 6084 is 78
(iii) 9025
By the division method
Taking 90 as first pair of digits and 25 as second pair of digits
Now taking 9 as divisor and quotient since square of 9 is smaller than first pair of digits
Bringing the remainder to the left side of the next pair
Now taking 18 as the first part of divisor and 5 as a second part of divisor and the quotient is equal to 8 as the product is equal to the new dividend
So the result is

	95
9	\[\overline {90} \]\[\overline {25} \]
+9	81
185	925
	925
	0

Therefore the square root of 9025 is 95

Note: In the above questions we used the division method the steps to use these methods are;
The first step to find the square root of the given number is to break the digits into pairs from right to left where each pair consist of 2 digits of a number
In the second step we start dividing the leftmost pair of digits where we take divisor and quotient the largest number which have square equal to or less than the leftmost pair of digits
For the step third we subtract the square of the divisor from the leftmost pair of digits and to have a new dividend we bring next pair of digits at the right side of remainder
In fourth step we consider the first part of new divisor as 2 times of the previous quotient and taking the second part such that the product of complete divisor and second part is equal or less than the new dividend and in this step the quotient is equal to the second part of new divisor
Then we repeat these steps again and again until we get the square root of the given number. Here the square root of a number is represented by the obtained quotient.