Page 61 - Start Up Mathematics_8 (Non CCE)

2. Squaring Numbers Close to 100
The rule says, ‘‘Whatever the extent of deficiency, lessen it still further to that very extent’’.

For example, let’s find the square of 97.
The answer of this has two parts.
The deficiency of 97 from 100 is “100 – 97 = 3”.
2
So, the second part of the answer is the square of “3”, i.e., (3) = 09
09
Answer =  
1st part 2nd part
The rule says, “To get the first part of the answer reduce the deficiency still further by the same extent”.
So, let’s reduce further the deficiency of 3 from 97, i.e., 97 – 3 = 94.

94 09
So, the answer is  
1st part 2nd part
2
\ (97) = 9,409
3. Squaring Numbers Just More Than 100
The rule says, “Whatever the extent of surplus, increase it further to that very extent”.
For example, let’s find the square of 107.
The answer of this has two parts.
The surplus of 107 from 100 is “107 – 100 = 7”.
2
So, the second part of the answer is the square of “7”, i.e., (7) = 49.
49
Answer =  
1st part 2nd part
The rule says, “To get the first part of the answer, increase the surplus still further by the same extent”.

So, let’s increase 107 further by 7, i.e., 107 + 7 = 114.
114 49
So, the answer is  
1st part 2nd part
2
\ (107) = 11,449

EXERCISE 3.3

1. Find the squares of the following numbers using the column method:
(a) 36 (b) 57 (c) 42 (d) 29 (e) 76
2. Find the squares of the following numbers using the observation method:
(a) 97 (b) 402 (c) 105 (d) 98 (e) 308
3. Find the squares of the following numbers using the diagonal method:
(a) 27 (b) 44 (c) 56 (d) 32 (e) 64
4. Find the squares of the following numbers using the easy method:
(a) 91 (b) 98 (c) 106 (d) 195 (e) 505
2
2
2
5. Find the squares of the following numbers using either (x + y) = x + 2xy + y or
2
2
2
(x – y) = x – 2xy + y .
(a) 199 (b) 103 (c) 202 (d) 395 (e) 998
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