1. Square
Least number
Add & Subtract

2. Incase of Subtraction, Subtract divisor from remainder
Example 1:
Find the least number, which must be subtracted from 180 to make it a perfect square.
Solution:
divisor
Step 1: Perform long division for finding square roots
Step 2: 180 is not a perfect square
There is a remainder 11
Step 3: Subtract remainder from divisor
180 – 11 = 169
132
Hence, the smallest number to be subtracted from 180 to make it a perfect square is 11.
is a perfect square
remainder
Incase of Subtraction, Subtract divisor from remainder

3. Incase of Subtraction, Subtract divisor from remainder
Example 2:
Find the least number, which must be subtracted from 360 to make it a perfect square.
Solution:
divisor
Step 1: Perform long division for finding square roots
Step 2: 360 is not a perfect square
There is a remainder 36
Step 3: Subtract remainder from divisor
360 – 36 = 324
182
Hence, the smallest number to be subtracted from 360 to make it a perfect square is 36.
remainder
is a perfect square
Incase of Subtraction, Subtract divisor from remainder

4. add 1 to quotient , square it and subtract it from the divisor
Example 3:
Find the least number, which must be added to 5607 to make it a perfect square.
Solution:
quotient
divisor
Step 1: Perform long division for finding square roots
Step 2: 5607 is not a perfect square
There is a remainder 131
This shows that quotient 742 < 5607
Step 3: Next perfect square is 752=5625
Step 4:Subtract divisor from 752
= 5625 – 5607= 18
Hence, the smallest number to be added to 5607 to make it a perfect square is 18.
remainder
Incase of addition,
add 1 to quotient , square it and subtract it from the divisor

5. add 1 to quotient , square it and subtract it from the divisor
Example 4:
Find the least number, which must be added to 6412 to make it a perfect square.
Solution:
quotient
divisor
Step 1: Perform long division for finding square roots
Step 2: 6412 is not a perfect square
There is a remainder 12
This shows that quotient 802 < 6412
Step 3: Next perfect square is 812=6561
Step 4: Subtract divisor from 812
= 6561 – 6412= 149
Hence, the smallest number to be added to 6412 to make it a perfect square is 149.
remainder
Incase of addition,
add 1 to quotient , square it and subtract it from the divisor

6. Try These:
1. Find the least number, which must be subtracted from 7250 to make it a perfect square.
2. Find the least number, which must be added to 7900 to make it a perfect square.