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Any easy method to find square of numbers?

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CBSE Tuition CBSE/Class 10/Mathematics

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Yes, there are. I am trying to explain step by step.Say we want the square of n = 67. First of all, the square of 7 is 49. Write 9 in the answer place and keep 4 for carrying over process.∴n^2 = 9Then, see that 6 and 7 form the number 67. Their product is 42. The rule says you have to double it.... read more

Yes, there are. I am trying to explain step by step.
Say we want the square of n = 67. First of all, the square of 7 is 49. Write 9 in the answer place and keep 4 for carrying over process.
∴n^2 = 9
Then, see that 6 and 7 form the number 67. Their product is 42. The rule says you have to double it. Hence you get double of 42 as 84. Also, you have 4 in your hand for carrying over. Together you get 84+4=88. Write the unit digit eight beside 9 and keep 10s digit 8 for next round carry-over process.
∴ n^2 = 89
Finally, the 10s digit is 6. Square it, and you will get 36. Plus you have 8 in your hand. Together we get 36+8, i.e. 44. Now write it beside 89, and we are done.
∴ 67^2 = 4489.
Try your self: 39^2, 23^2, 52^2.
 
Verify your answer using a calculator.
 
For squaring three digits or more, there is procedure indeed, but I can't explain them here within short place. 
 
Although I can show you some other special technique for squaring 2 digit numbers of special types. 
 
1. If the number ends with 5: 
Let's say we need to square 85. First, write 25 straight forward in answer place. 
85^2 = 25
 
Then, note that after ignoring five we are left with the number 8 in the given number 85. The next number of 8 is 9. The rule says to make the product which is in our present case is 8 x 9, i.e. 72.
 
Write it down, and we are done.
85^2 = 7225.
Similarly, 95^2 = 9025 because 9 x 10 = 90 and 25 already is written etc.
115^2 = 13225 because 11 x 12 = 132. Etc
 
2. If the number is near to 100.
Let's say we need to square 93. 
 
The difference between 93 and 100 is 7. The rule says to write down the square of 7 first, which is here 49.
Next, decrease 93 by 7. Which gives 86. Hence the final answer becomes 
93^2=8649.
Similarly, 95^2 is 9025 because the difference between 95 and 100 is 5. The square of 5 is 25, and if we decrease 95 by 5, we shall get 90
 Together we thus obtain 
95^2= 9025.
Notice we have achieved the same already before by using the general squaring technique explained above.
 
Caution. Suppose we want to square 98. This time doesn't be tempted to write 964. That's not correct. While you are squaring the difference between 100 and the given number, make sure the answer occupies exactly two places only. If not, use 0 to fill up the lattice. Hence 98^2 is not 964 but in 9604.
 
Similarly, for 88^2, first, write down the square of the difference which is 12^2, i.e. 144. But this time it is a three-digit answer. So keep the last two digits and carry over the excess digit which is 1 in this present case. Now decrease 88 by 12, and we get 76. Added by carried over one we get 77. Hence 88^2 = 7744.
 
There are more so many special rules. But we can discuss them some other days.
 
Take care.

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1 Comments

More than 22 years of experience of teaching Mathematics to classes 12, 11, 10 and 9 in CBSE schools

Many shortcuts can be found at Google or You-tube.But please remember that any shortcut will be applicable to a limited number of questions only, falling under a certain category.In general, being good at multiplication and knowing as many tables as possible will only help to be fast and confident.There... read more

Many shortcuts can be found at Google or You-tube.
But please remember that any shortcut will be applicable to a limited number of questions only, falling under a certain category.
In general, being good at multiplication and knowing as many tables as possible will only help to be fast and confident.
There is no shortcut to success, you know!

read less
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3 Year's of Experience in Teaching Math & Physics to class 8 to 12 student's

Stick with the basic method. Also you can try vedic math shortcuts for certain numbers only.
Comments

Tutor

The easiest way is to do the prime factorization.
Comments

A more of a mentor, friend and a guide.

You can refer to YouTube. There are many such available.
Comments

Concpet developer

Vedic Maths But if you follow basics, it will be easy. Praticse regularly like an activity.
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Improve analytical skills of students for mathematics

The easy method is square of last digit i.e 5*5 and n(n+1) of remaining digits to the left so even square of 125 is 15625 i.e 12*13 on the left and 5*5 on the right i.e 15625.
1 Comments

A Mathematician With 2-3 Years of Experience Teaching

By Checking the Digit at the Units Place. There will be a pattern.
Comments

Easy methods and tricks are not valid all the time, so basic method are always applicable.
Comments

Tutor with 2 Years of Experience

Yes there are many methods to find out the square of a number. For 2 digit numnber, you can simply multiply. It is easier only. For 3 digit or more you cancalculate by vadic multiplication method that will be easier.. Thank you.
Comments

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