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19 Dec 2013, 23:13
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Hi All,
It might be a long post,But I will say it is worth spending 5 min here.You will surely get benefitted from this. I am preparing for GMAT and found a way to calculate squares in very minimal time.
Please take a walk through from steps::
Step 1: Remember the Square from 1 to 10.
1--->1
2--->4
3--->9
4--->16
5--->25
6--->36
7--->49
8--->64
9--->81
10--->100
I hope its easy to remember 1 to 10
.
Now for next numbers follow this approach:
To calculate square 11 to 19
Consider we want to calculate square of 12.
1. Add unit digit to number in this case – 12+2 = 14.(AB)
2. Write square of unit digit in this case it is 4.(C)
3. Write digits ABC as answer, so the answer is 144.
Point to remember answer will always be of three digits.
Consider number 17 (in which 7 square is 49 i..e of two digits)
1. Add unit digit in this case to number in this case – 17 + 7 = 24(AB).
2. Write square of unit digit in this case it is 49.(C)
3. So while writing answer you should add 4 from 49 to 4 from 24.
4. So answer will be 289.
The whole above calculation is possible because base is 10.
Now consider 21 to 29
Now base is 20.
Consider number : 23
1. Add unit digit to number = 23+3 = 26
2. Now double this number = 52 (AB) (we are doubling this number because the base is 10 *2 ==20)
3. Now square the unit digit which is 9.(C)
4. So write answer as ABC – 529.
Consider one more number 27.(Asked in one of the comment)
1. Add unit digit 27+7 = 34
2. Now double this number : 68(AB)
3. Now square unit digit : 49.(C)
4. Now add 4 of 49 to 8 of 68. 729
5. So 729 will be the answer.
Easy Way to Calculate the square of 30 to 80:
Remember Square (50) = 2500
If you want to find the square of 49
Step1: The difference between number and 50 = 1
Step2: Reduce the difference from 25, you will get 24 here
Step3: Square the difference and write in front of Step 2.
Step1: 50-49=1
Step2: 25-1=24
Step3: Square (1) =1
Step4:2401 is the answer.
Example 2: Square (48)
Step1:50-48 = 2
Step2: 25-2=23
Step3: Square (2) = 4
Step4:2304 is the answer.
To consider a number more than 50
In Step 1 you need to subtract 50 from the number you want to square. In Step 2 you need to add.
Square ( 51)
Step1: 51-50=1
Step2: 25+1=26
Step3: Square (1) =1
Step4:2601 is the answer.
Your view and comments are welcome.
Thanks,
AB
It might be a long post,But I will say it is worth spending 5 min here.You will surely get benefitted from this. I am preparing for GMAT and found a way to calculate squares in very minimal time.
Please take a walk through from steps::
Step 1: Remember the Square from 1 to 10.
1--->1
2--->4
3--->9
4--->16
5--->25
6--->36
7--->49
8--->64
9--->81
10--->100
I hope its easy to remember 1 to 10
.Now for next numbers follow this approach:
To calculate square 11 to 19
Consider we want to calculate square of 12.
1. Add unit digit to number in this case – 12+2 = 14.(AB)
2. Write square of unit digit in this case it is 4.(C)
3. Write digits ABC as answer, so the answer is 144.
Point to remember answer will always be of three digits.
Consider number 17 (in which 7 square is 49 i..e of two digits)
1. Add unit digit in this case to number in this case – 17 + 7 = 24(AB).
2. Write square of unit digit in this case it is 49.(C)
3. So while writing answer you should add 4 from 49 to 4 from 24.
4. So answer will be 289.
The whole above calculation is possible because base is 10.
Now consider 21 to 29
Now base is 20.
Consider number : 23
1. Add unit digit to number = 23+3 = 26
2. Now double this number = 52 (AB) (we are doubling this number because the base is 10 *2 ==20)
3. Now square the unit digit which is 9.(C)
4. So write answer as ABC – 529.
Consider one more number 27.(Asked in one of the comment)
1. Add unit digit 27+7 = 34
2. Now double this number : 68(AB)
3. Now square unit digit : 49.(C)
4. Now add 4 of 49 to 8 of 68. 729
5. So 729 will be the answer.
Easy Way to Calculate the square of 30 to 80:
Remember Square (50) = 2500
If you want to find the square of 49
Step1: The difference between number and 50 = 1
Step2: Reduce the difference from 25, you will get 24 here
Step3: Square the difference and write in front of Step 2.
Step1: 50-49=1
Step2: 25-1=24
Step3: Square (1) =1
Step4:2401 is the answer.
Example 2: Square (48)
Step1:50-48 = 2
Step2: 25-2=23
Step3: Square (2) = 4
Step4:2304 is the answer.
To consider a number more than 50
In Step 1 you need to subtract 50 from the number you want to square. In Step 2 you need to add.
Square ( 51)
Step1: 51-50=1
Step2: 25+1=26
Step3: Square (1) =1
Step4:2601 is the answer.
Your view and comments are welcome.
Thanks,
AB
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19 Dec 2013, 23:22
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I have an easier way. Just remember the squares of all numbers from 1 to 50 like I have 
Much more easier and reliable. Learn by rote.
Much more easier and reliable. Learn by rote.
23 Dec 2013, 21:59
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As far as the GMAT is concerned, my sense is that they are only expecting one to recognize squares of numbers up to 16. Other than that they do expect students to be able to quickly see that 900 is square of 30 etc. Anything beyond is irrelevant in my opinion. If one does need to find square of say 37 on the GMAT(highly unlikely), then just resort to multiplication. I would recommend staying away from memorizing such rules, it is too much burden on one's brain and is really not necessary for the GMAT.
Dabral
Dabral
. 
