MATHS

1. Find square of a number that ends with digit 5. For example what is value of 5 x 5, 15 x 15 etc..
In 15 x 15, 1 appears before 5. Add one(1) to 1, which is 2. Now multiply 2 and 1, which is 2. Then write 25 after 2.
So square of 15 = (1x2)25 = 225
Similarly
25 X 25 = (2x3) before 25 = 625
35 X 35 = (3x4) before 25 = 1225
45 X 45 = (4x5) before 25 = 2025
55 X 55 = (5x6) before 25 = 3025
65 X 65 = (6x7) before 25 = 4225
Find square of a number that has all 1. For example what is value of 11 x 11, 111 x 111 etc..
In 111 x 111, 1 appears 3 times. Now write numbers in ascending order upto 3. Then write in descending order
upto 1.
So square of 111 is ascending123decending21
Similarly
11 X 11 = 121
111 X 111 = 12321
1111 X 1111 = 1234321
11111 X 11111 = 123454321
111111 X 111111 = 12345654321
Find square of two digit number that begins with 5. For example what is value of 52 X 52, 59 x 59
etc..
In 59 x 59, 5 is first digit and 9 is second digit.
Square of first digit is 25
Square of second digit is 81
Now square of 59 will be (Square of first digit plus second digit) join (Square of second digit)
So square of 59 will be (25 + 9) join (81) = 3481
Similarly
51 X 51 = (25+1) join (01) = 2601
52 X 52 = (25+2) join (04) = 2704
56 X 56 = (25+6) join (36) = 3136
57 X 57 = (25+7) join (49) = 3249
7 Easy Math Tricks
Downloaded from www.icbse.com

2. 58 X 58 = (25+8) join (64) = 3364
Find square of two digit number that begins with 9. For example what is value of 92 X 92, 99 x 99
etc..
In 98 x 98, 9 is first digit and 8 is second digit.
Subtract 98 from 100, 100 - 98 = 2
Square of 2 is 04
Subtract 2 from 98 from 98, 98 - 2 = 96
Now square of 98 will be 96 second digit) join (04)
So square of 98 will be 9604
Similarly
91 X 91 = (91-9) join (9X9) = (82) join (81) = 8281
94 X 94 = (94-6) join (6X6) = (88) join (36) = 8836
96 X 96 = (96-4) join (4X4) = (92) join (16) = 9216
97 X 97 = (97-3) join (3X3) = (94) join (09) = 9409
Find square of two digit number that ends with 1. For example what is value of 21 X 21, 61 x 61 etc..
In 61 x 61, 6 is first digit and 1 is second digit.
Subtract 1 from 61, 61 - 1 = 60
Square of 60 is 3600
Add 60 and 60, 60 + 60 = 120
Now square of 61 will be (Square of 60) plus (Add 60 and 60) plus (1)
So square of 61 will be 3600 + 120 + 1 = 3721
Similarly
91 X 91 = (90 x 90) plus (90 + 90) plus 1 = 8100 + 180 + 1 = 8281
71 X 71 = (70 x 70) plus (70 + 70) plus 1 = 4900 + 140 + 1 = 5041
51 X 51 = (50 x 50) plus (50 + 50) plus 1 = 2500 + 100 + 1 = 2601
31 X 31 = (30 x 30) plus (30 + 30) plus 1 = 900 + 60 + 1 = 961
Find square of number that are between 1000 and 1030. For example what is value of 1009 X 1009,
1025 x 1025 etc..
In 1009 x 1009, 1 is first digit, 0 is second digit, 0 is third digit and 9 is fourth digit.
The square will be of 7 digit. i.e _ _ _ _ _ _ _
This first two digit are 10. i.e 10 _ _ _ _ _
Downloaded from www.icbse.com

3. Subtract 1000 from 1009 and multiply the result by 2, which is 9 x 2 = 18.
Now third and fourth digit are 18. i.e 1018 _ _.
Subtract 1000 from 1009 and square it, which is 9 x 9 = 81.
Now fifth, sixth and seventh digit will be 081.
So square of 1009 will be 1018081
Similarly
1025 X 1025 = (10)join(2x25) join(25x25) = 1050625
1019 X 1019 = (10)join(2x19) join(19x19) = 1038361
Find square of a number that has all 9. For example what is value of 99 x 99, 999 x 999 etc..
In 999 x 999, 9 appears 3 times. So write 9 two times, 8 one time, 0 two times and 1 one time. Then write in
descending order upto 1.
i.e if 9 appears n times then answer is (n-1 times 9) join (one time 8) join (n-1 times 0) join (one time 1).
So square of 999 is (2 times 9) join (one time 8) join (2 times 0) join (one time 1) = 998001
Similarly
99 X 99 = (1 times 9) join (one time 8) join (1 times 0) join (one time 1) = 9801
99999 X 99999 = (4 times 9) join (one time 8) join (4 times 0) join (one time 1) = 9999800001
Downloaded from www.icbse.com