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TRICK TO FIND SQUARES OF NUMBERS ENDING WITH 5,9,1

Square of numbers ending with 5 Formula for calculating square ending with 5 is easy.

$$\begin{array} { l l } & 85 \\ \times & 85 \\ \hline \\ & 7225 \end{array}$$

Steps

• Multiply 5 by 5 and put composite digit 25 on the right hand side.
• Add 1 to the upper left hand side digit i.e. 8 i.e. 8+1=9
• Multiply 9 to the lower hand digit 8, i.e. 9*8=72
• Our answer is 7225.

Using this method we can find out square of the number. Now let’s have a look at method of calculating square of adjacent number.

Forward Method
We know method to find square of a number ending with 5., say Square of 75=5625, then just have a look to find square of 76.
75’s square=5625(known)
76’square=75’square+ (75+76) =5625+151=5776.
So square of 76 is 5776.

Steps

• Steps are simple. The format shown above is self explanatory. But still I am explaining it.
• 75’square=5625 is known
• Add (75+76=151) to this to get 76’square
• 76’square=5776.

Reverse Method
As like forward method for calculating square of number which is 1 more than the given number whose square is known, we have reverse method to find square.
Now let me explain in detail the Reverse approach through which You will able to find out squares of a number which is one less than given number.
Consider the following example:
Suppose we know square of a number, say, 70; how to find square of 69?
(70)’square=4900(known)
(69)’square=4900-(69+70) =4900-139
=4761.
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Note by Prajwal Kavad
7 years, 2 months ago

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## Comments

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Nice tricks Sir!

- 1 year, 1 month ago

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