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Squaring Tricks
Easy ways for squaring a big number.

Division Tricks
How can you find out whether a given large number is divisible by another number without remainder?

Magic Numbers
Some methods of repeating numbers. This will be interesting for you.

Multiplication Tricks
Easy methods to multiply two given numbers.

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Squaring Tricks

Squaring numbers is very important in maths. But it is very hard and boring when it comes to square large numbers. So, I will teach you some easy ways to square large numbers.

Let's start with numbers 51 - 100.

Subtract the number you want to square from 100. (100 - a)
Take this difference and subtract it from the number you want to square. [a - (100 - a)].
Multiply the answer by 100. 100[a - (100 - a)]
Square the difference, the answer from step 1. Add that number to your answer.
100[a - (100 - a)] + (100 - a)²

Example 1 - 96²

100 - 96 = 4.
96 - 4 = 92. 92 x 100 = 9200
4² = 16. Add 16 to 9200.
Now, you have a answer. It is 9,216.

Example 2 - 84²

100 - 84 = 16
84 - 16 = 68. 68 x 100 = 6800.
16² = 256. Add 256 to 6800
The answer is 7,056

Now, let's move on to numbers greater than 100. Here are the steps and an example.

Subtract 100 from the number you want to square (a - 100 )
Take the difference and add it to the number you want to square. [a + (a - 100)].
Multiply the answer by 100. 100[a + (a - 100)]
Square the difference, the answer from step 1. Add the number to your answer.
100[a + (a - 100)] + (a - 100)²

Example 3 - 112²

112 - 100 = 12
112 + 12 = 124. 124 x 100 = 12400.
12² = 144. Add 144 to 12400.
The answer is 12,544.

Let's use the same rule for numbers around 1000. Here are 2 examples:

1000[a - (1000 - a)] + (1000 - a)² and 1000[a + (a - 1000)] + (a - 1000)²

Example 4 - 996²

1000 - 996 = 4
996 - 4 = 992. 992 x 1000 = 992000.
4² = 16. Add it to the answer.
Now it is 992,016.

Example 5 - 1007²

1007 - 1000 = 7
1007 + 7 = 1014. 1014 x 1000 = 1014000.
7² = 49.
Answer: 1,014,049

There is another simple way to square any number ending in 5.

Omit the 5, and multiply the number as it will then stand, by the next higher number, and append 25 to the product.

Example 6 - 25²

Omit the 5, then multiply 2 by the next higher number, 3: 2 x 3 = 6.
Finally, append 25. That's the answer: 625.

Let's learn to square any number contain 1/2

Multiply the whole number by the next higher whole number and append 1/4 to the product.
a(a + 1) + 1/4

Example 7 - (6 1/2)²

Multiply 6 by 7. It is 42. Then add 1/4. Answer is 42 1/2.