Finding Squares for Numbers – Simple and Quick Technique

Finding Squares for Numbers – Simple and Quick Technique

A quick question:

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What is 82?

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Try answering without your calculator. (Answer: 64)

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Squaring single digit numbers in your head is not that difficult if you know the multiplication tables. Squaring large numbers is not so easy. Continue reading this article for an easy method.

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Arithmetic does not always have to be done from right-to-left—in fact plenty of people do it the other way around. If you see a problem like 32+18, adding it in your head from left to right lets you see 40 first (30 + 10), and then the 10 (2 + 8). Whereas if you had gone right to left, you’d take a bit more time with carry overs and further additions. Going left to right can also be used to simplify multiplication.

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 But what if you want to square a number like 332? Let us look at an easy method

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Case 1

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Let us take numbers with 5 as last digit- The squares of numbers ending with 5 will always have 25 as the last two digits. The remaining digits of the square are the product of the remaining part of the number and its next higher number.

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Example: 652 = 4225 (Since, 6 x 7 = 42)

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Case 2

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Let us take multiplication of two numbers with 5 as last digit.

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The last two digits will be 25, if the remaining digits in both the numbers are odd or even

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and

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It is 75, if one digit is odd and another is even.

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The remaining digits will be:

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Product of the remaining numbers + sum of the remaining numbers and their average (lesser integer if it has a decimal).

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Example: 65 x 75 = 4875 (Since, 6 x 7 + 6 = 48)

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Case 3

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The squares of numbers which are close to other numbers (for which squares are known), can be easily calculated as shown in the following examples:

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662 can be written as (65 + 1)2

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Now, it is simple to find the answer as 652 + 66th odd number (nth odd number= 2n-1)

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652 can be found using the above discussed method.

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652 is 4224 + 66 x 2 – 1(2n-1) = 4356

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Comment your answer for the following questions. Be quick!!

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  1. 852 = ________________
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  3. 1452 = ________________
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  5. 1022 = ________________
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  7. 512 = ________________
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