Look at the list of two-digit numbers below and find out a pattern that you might notice:
052 = 25
152 = 225
252 = 625
352 = 1,225
452 = 2,025
552 = 3,025
652 = 4,225
752 = 5,625
852 = 7,225
952 = 9,025
2) Their corresponding square values are also, always end with '25' (the last two digits are always the digits 2 and 5)
3) With another pattern that might 'amuse' you. You want to find it out?
Let us rearrange the appearance of the square values of the two-digit numbers ending in 5 according to the first golden rule of SSQ - "the count of digits doubles as you square a number".
INDEX SQUARES OF TWO-DIGIT NUMBERS ENDING IN FIVE
052 = 00'25
152 = 02'25
252 = 06'25
352 = 12'25
452 = 20'25
552 = 30'25
652 = 42'25
752 = 56'25
852 = 72'25
952 = 90'25
Check This Out
1) The first two digits of the square of 05 are 0 0 and of course, its last two digits are 2 and 5. Take note that 0 in 052 when "multiplied to a number next to it, higher by 1", will still give a product equal to zero (0). (Take note: Any number multiplied by zero is always equal to zero)
0 x 1 = 0 (052 = 00'25) (1 is next to 0, higher by 1)
2) The first two digits of the square of 15 are 0 2 and of course, its last two digits are 2 and 5. Take note that 1 in 152 when "multiplied to a number next to it, higher by 1", will give us a product equal to 2
1 x 2 = 2 (152 = 02'25) (2 is next to 1, higher by 1)
3) The first two digits of the square of 25 are 0 6 and of course, its last two digits are 2 and 5. Take note that 2 in 252 when "multiplied to a number next to it, higher by 1", will give us a product equal to 6
2x 3 = 6 (252 = 06'25) (3 is next to 2, higher by 1)
Repeating the same pattern for the other numbers, we can now easily get the square of any two-digit number ending in 5.
952 = ?
Step 1: Simply write down the last two digits as 2 and 5
952 = _ _'25
Step 2: Multiply the first digit (in this case, 9) by a number higher by 1 to it
Since 9 + 1 = 10
9 x 10 = 90
Step 3: The product (90) will be the first two digits that will complete the square value
952 = 90'25
Exercise: (Do It Yourself)
1) Prove that 45 is indeed equal to 20'25 using the 'Digit Per Digit SSQ Method'
2) 2572 = ?
3) 45,652 = ?
4) 35, 2572 = ?
(Hint: For questions 2 - 4, Try to use Groupee Squaring)
Check This Out
1) The first two digits of the square of 05 are 0 0 and of course, its last two digits are 2 and 5. Take note that 0 in 052 when "multiplied to a number next to it, higher by 1", will still give a product equal to zero (0). (Take note: Any number multiplied by zero is always equal to zero)
0 x 1 = 0 (052 = 00'25) (1 is next to 0, higher by 1)
2) The first two digits of the square of 15 are 0 2 and of course, its last two digits are 2 and 5. Take note that 1 in 152 when "multiplied to a number next to it, higher by 1", will give us a product equal to 2
1 x 2 = 2 (152 = 02'25) (2 is next to 1, higher by 1)
3) The first two digits of the square of 25 are 0 6 and of course, its last two digits are 2 and 5. Take note that 2 in 252 when "multiplied to a number next to it, higher by 1", will give us a product equal to 6
2x 3 = 6 (252 = 06'25) (3 is next to 2, higher by 1)
Repeating the same pattern for the other numbers, we can now easily get the square of any two-digit number ending in 5.
952 = ?
Step 1: Simply write down the last two digits as 2 and 5
952 = _ _'25
Step 2: Multiply the first digit (in this case, 9) by a number higher by 1 to it
Since 9 + 1 = 10
9 x 10 = 90
Step 3: The product (90) will be the first two digits that will complete the square value
952 = 90'25
Exercise: (Do It Yourself)
1) Prove that 45 is indeed equal to 20'25 using the 'Digit Per Digit SSQ Method'
2) 2572 = ?
3) 45,652 = ?
4) 35, 2572 = ?
(Hint: For questions 2 - 4, Try to use Groupee Squaring)
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