There are so many calculations to be performed and whats to be done when we don't have a calculator. Beta-Theta brings to you an assorted collection of useful Tricks that will surely help you increase your problem solving speed. Some of the tricks below are a little tough so please pay extra attention while reading them. We have more tricks on page 1.

Trick 2 : Squaring numbers in the hundreds.

If the number to be squared is 106:
Square the last two digits (no carry): 6 x 6 = 36: _ _ _ 3 6
Add the last two digits (06) to the number: 106 + 6 = 112: 1 1 2 _ _
So 106 x 106 = 11236.
See the pattern?

If the number to be squared is 112:
Square the last two digits (keep carry 1): 12 x 12 = 144: _ _ _ 4 4
Add the last two digits (12) plus the carry (1) to the number:
112 + 12 + 1 = 125: 1 2 5 _ _
So 112 x 112 = 12544.

Trick 3 : Squaring a number in the two hundreds.

Choose a number in the 200s (practice with numbers under 210, then progress to larger ones).
Square the first digit = 4: __4 _ _ _ _
The next two digits will be 4 times the last 2 digits: _ X X _ _
The last two places will be the square of the last digit: _ _ _ X X

Example:
If the number to be squared is 206:
The first digit is 4: 4 _ _ _ _
The next two digits are 4 times the last two digits :
4 x 6 = 24: _ 2 4 _ _
Square the last digit: 6 x 6 = 36: _ _ _ 3 6
So 206 x 206 = 42436.

For larger numbers work right to left:

Square the last two digits (keep the carry): _ _ _ X X
4 times the last two digits + carry: _ X X _ _
Square the first digit + carry: X _ _ _ _

See the pattern?

If the number to be squared is 225:
Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
4 times the last two digits + carry:
4x25 = 100; 100+6 = 106 (keep 1): _ 0 6 _ _
Square the first digit + carry:
2x2 = 4; 4+1 = 5: 5 _ _ _ _
So 225 x 225 = 50625.

Trck 4 : Squaring a number in the three hundreds

Choose a number in the 300s (practice with numbers under 310, then progress to larger ones).
Square the first digit = : 9 _ _ _ _
The next two digits will be 6 times the last 2 digits: _ X X _ _
The last two places will be the square of the last digit: _ _ _ X X
Example:
If the number to be squared is 309:
The first digit is 9: 9 _ _ _ _
The next two digits are 6 times the last digit:
6 x 9 = 54: _ 5 4 _ _
Square the last digit: 9 x 9 = 81: _ _ _ 8 1
So 309 x 309 = 95481.

For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ X X
6 times the last two digits + carry: _ X X _ _
Square the first digit + carry: X _ _ _ _

See the pattern?

If the number to be squared is 325:
Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
6 times the last two digits + carry:
6x25 = 150; 150+6 = 156 (keep 1): _ 5 6 _ _
Square the first digit + carry:
3x3 = 9; 9+1 = 10: 1 0 _ _ _ _
So 325 x 325 = 105625.

Trick 5: Squaring numbers in the four hundreds

Choose a number in the 400s (keep the numbers low at first; then progress to larger ones).
The first two digits of the square are 16: 1 6 _ _ _ _
The next two digits will be 8 times the last 2 digits: _ _ X X _ _
The last two places will be the square of the last two digits: _ _ _ _ X X
Example:
If the number to be squared is 407:
The first two digits are 16: 1 6 _ _ _ _
The next two digits are 8 times the last 2 digits:
8 x 7 = 56: _ _ 5 6 _ _
Square the last digit: 7 x 7 = 49: _ _ _ 4 9
So 407 x 407 = 165,649.

For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ _ X X
8 times the last two digits + carry: _ _ X X _ _
16 + carry: X X _ _ _ _

See the pattern?

If the number to be squared is 425:
Square the last two digits (keep the carry):
25 x 25 = 625 (keep 6): _ _ _ _ 2 5
8 times the last two digits + carry:
8 x 25 = 200; 200 + 6 = 206 (keep 2): _ _ 0 6 _ _
16 + carry: 16 + 2 = 18: 1 8 _ _ _ _
So 425 x 425 = 180,625.

Trick 6 : Squaring numbers in the five hundreds

Choose a number in the 500s (start with low numbers at first; then graduate to larger ones).
The first two digits of the square are 25: 2 5 _ _ _ _
The next two digits will be 10 times the last 2 digits: _ _ X X _ _
The last two places will be the square of the last two digits: _ _ _ _ X X
Example:
If the number to be squared is 508:
The first two digits are 25: 2 5 _ _ _ _
The next two digits are 10 times the last 2 digits:
10 x 8 = 80: _ _ 8 0 _ _
Square the last digit: 8 x 8 = 64: _ _ _ 6 4
So 508 x 508 = 258,064.

For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ _ X X
10 times the last two digits + carry: _ _ X X _ _
25 + carry: X X _ _ _ _

See the pattern?

If the number to be squared is 525:
Square the last two digits (keep the carry):
25 x 25 = 625 (keep 6): _ _ _ _ 2 5
10 times the last two digits + carry:
10 x 25 = 250; 250 + 6 = 256 (keep 2): _ _ 5 6 _ _
25 + carry: 25 + 2 - 27: 2 7 _ _ _ _
So 425 x 425 = 275,625.

It is quite possible that you have problems in understanding some of the tricks mentioned in this page. Please use our Reference Forums for help in understanding any of the above tricks or to ask for help in any other topic.