Beat Your Calculator - Squaring a 2-digit number beginning with , & 9

aragon · #1 (**permalink**) 09-13-2007, 09:18 AM

Squaring a 2-digit number beginning with 1

1. Take a 2-digit number beginning with 1.
2. Square the second digit
(keep the carry) _ _ X
3. Multiply the second digit by 2 and
add the carry (keep the carry) _ X _
4. The first digit is one
(plus the carry) X _ _

Example:

1. If the number is 16, square the second digit:
6 × 6 = 36 _ _ 6
2. Multiply the second digit by 2 and
add the carry: 2 × 6 + 3 = 15 _ 5 _
3. The first digit is one plus the carry:
1 + 1 = 2 2 _ _
4. So 16 × 16 = 256.

See the pattern?

1. For 19 × 19, square the second digit:
9 × 9 = 81 _ _ 1
2. Multiply the second digit by 2 and
add the carry: 2 × 9 + 8 = 26 _ 6 _
3. The first digit is one plus the carry:
1 + 2 = 3 3 _ _
4. So 19 × 19 = 361.

Squaring a 2-digit number beginning with 5

1. Take a 2-digit number beginning with 5.
2. Square the first digit.
3. Add this number to the second number to find the first part of the answer.
4. Square the second digit: this is the last part of the answer.

Example:

1. If the number is 58, multiply 5 × 5 = 25 (square the first digit).
2. 25 + 8 = 33 (25 plus second digit).
3. The first part of the answer is 33 3 3 _ _
4. 8 × 8 = 64 (square second digit).
5. The last part of the answer is 64 _ _ 6 4
6. So 58 × 58 = 3364.

See the pattern?

1. For 53 × 53, multiply 5 × 5 = 25 (square the first digit).
2. 25 + 3 = 28 (25 plus second digit).
3. The first part of the answer is 28 2 8 _ _
4. 3 × 3 = 9 (square second digit).
5. The last part of the answer is 09 _ _ 0 9
6. So 53 × 53 = 2809.

Squaring a 2-digit number beginning with 9

1. Take a 2-digit number beginning with 9.
2. Subtract it from 100.
3. Subtract the difference from the original number:
this is the first part of the answer.
4. Square the difference: this is the last part of the answer.

Example:

1. If the number is 96, subtract: 100 - 96 = 4, 96 - 4 = 92.
2. The first part of the answer is 92 _ _ .
3. Take the first difference (4) and square it: 4 × 4 = 16.
4. The last part of the answer is _ _ 16.
5. So 96 × 96 = 9216.

See the pattern?

1. For 98 × 98, subtract: 100 - 98 = 2, 98 - 2 = 96.
2. The first part of the answer is 96 _ _.
3. Take the first difference (2) and square it: 2 × 2 = 4.
4. The last part of the answer is _ _ 04.
5. So 98 × 98 = 9604.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Math Tricks - Beat The Calculator	aragon	General Knowledge	12	09-24-2008 11:38 AM
Multiplication Tips helps you to beat calculator	aragon	General Knowledge	3	08-14-2007 09:41 PM
Your New Beginning Sikandar107	Saira	Sentiments Express	27	06-17-2007 06:40 PM
Zakat Calculator	RAHEN	The Spiritual Heaven	2	10-19-2006 01:28 AM
Digit 3 and Pramod Mahajan - Intresting and Must Read	Bluehacks	General Knowledge	6	08-25-2006 09:12 PM