Yesterday I have shared you how to find Square of a number in Lesson One. Today I am sharing you the last rule and this is very important. By this rule you can fine square of any number. Let’s start.

## Shortcut to Find Square of A Number: Final Lesson

At first, separate the numbers like “Numbers Close to 50”, “Numbers Close to 1000”, “Numbers Close to 150”, “Numbers Close to 200”, “Numbers Close to 250”, “Numbers Close to 300”, and so on.

In previous lesson, you found the square of 10, 11 &15, 20, 21 & 25, 30, 31 & 35 so on. Now we find the square of the rest numbers. You may use today’s rule for all numbers. But, I prefer Rules of Lesson One for these numbers.

#### Rule: 1 Number Closes to 50

###
25 __+__ X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )
If we find the square of 53 (close to 50), then

53

^{2 }= 25__+__X | X^{2}
53

^{2 }= 25 + 3 | 3^{2}
53

53^{2 }= 28 | 09^{2 }= 2809

If we find the square of 53 (close to 50), then

46

^{2 }= 25__+__X | X^{2}
46

^{2 }= 25 - 4 | 4^{2}
46

^{2 }= 21 | 16
46

^{2 }= 2116#### Rule: 2 Number Closes to 100

###
100 __+__ 2X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )If we find the square of 104 (close to 100), then

104

^{2 }= 100__+__2X | X^{2}
104

^{2 }= 100 + 2.4 | 4^{2}
104

^{2 }= 100 + 8 | 16
104

^{2 }= 10816If we find the square of 92 (close to 100), then

92

^{2 }= 100__+__2X | X^{2}
92

^{2 }= 100 – 2.8 | 8^{2}
92

^{2 }= 100 -16 | 64
92

^{2 }= 84 | 64
92

^{2 }= 8464#### Rule: 3 Number Closes to 150

###
225 __+__ 3X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )If we find the square of 167 (close to 150), then

167

^{2 }= 225__+__3X | X^{2}
167

^{2}= 225 + 3.17 | 17^{2}
167

^{2 }= 225 + 51 | 289
167

167^{2}= 276 | 289 (add 2 with 6, makes 8)^{2}= 27889

If we find the square of 134 (close to 150), then

134

^{2 }= 225__+__3X | X^{2}
134

^{2 }= 225 – 3.16 | 16^{2}
134

^{2 }= 225 - 48 | 256
134

^{2 }= 177 | 256 (add 2 with 7, makes 9)
134

^{2 }= 17956You can try it for other numbers. Rules are given below:

#### Rule: 4 Number Closes to 200

###
400 __+__ 4X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )#### Rule: 5 Number Closes to 250

###
625 __+__ 5X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )#### Rule: 6 Number Closes to 300

###
900 __+__ 6X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )#### Rule: 7 Number Closes to 350

###
1225 __+__ 7X | X^{2}

(X takes -Value when the number is below 50 or vice versa & the digit will be two after | )Try it for numbers close to 400, 450, 500, 550 so on.

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