Think Outside The Book
Calculating Squares
Hi,
With this series of articles I would like to discuss a few fundas related to numbers / math that I have picked up over the years. We all have encountered questions in which if we knew the squares, we would have saved a few precious seconds. I always felt that if I was just a little bit faster, I might have done one more question in the exam. I am not saying that the fundas below would improve you drastically but I am sure you would find them a step in the right direction. I will start off with a simple funda.
How to calculate square of a number close to 50
This technique will work only for numbers which lie in the range [41,59] both ends included.
Funda - If the distance of the number from 50 is ‘x’, the last two digits will be x^2 and the first two digits will be 25+x. Let us check it out with an example.
#Suppose we want to calculate 54^2. The distance from 50 is 4.
ð The first two digits would be 25+4 = 29
ð The last two digits would be 4^2 = 16
ð The square of 54 would be 2916.
#Suppose we want to calculate 43^2. The distance from 50 is (-7).
ð The first two digits would be 25 + (-7) = 18
ð The last two digits would be (-7)^2 = 49
ð The square of 43 is 1849.
Now I guess you should be able to calculate the squares of numbers close to 50. I recommend that you practice it in your head without using a pen or paper.
How to calculate square of a number ending in 5
This technique will work for all numbers which end in 5. This will not work for numbers which end in other digits.
Funda – If we remove the last digit ‘5’ from our number and are left with x, then the square will be [Product of x and x+1]25.
#Suppose we want to calculate 65^2.
ð We remove 5 from our number, we are left with 6.
ð Product of 6 and 7 is 42
ð The square of 65 is 4225
#Suppose we want to calculate 195^2
ð We remove 5 from our number, we are left with 19
ð Product of 19 and 20 is 380
ð The square of 195 is 38025
I very strongly believe that just knowing more and more fundas is not going to help until and unless you practice them. So work on these ideas.
This post was published originally on FreshersWorld.
| This entry was posted by Handa on July 28, 2010 at 12:35 AM, and is filed under CAT, CAT 2010, Math Funda, Online CAT, Quantitative Aptitude. Follow any responses to this post through RSS 2.0. You can leave a response or trackback from your own site. |
about 1 month ago
Nice Simplification.
A word of caution for Method1:
1)How to calculate square of a number close to 50:
Its (50+x)^2=2500+x^2+2*50*x
=(25+x)*100+x^2
So,for this method to work,x^210<x<10
So this method will work for all squares from 41 to 59.
2)Working for Method2:
x5^2,where as said by Handa,x can be anything,
x5^2=(x*10+5)^2=100x^2+25+100^x
=100x(x+1)+25
which proves what Handa has stated in simple words:)
Once again,the point is working can be understood once,but once attempting question,only the method should be in mind:)
about 1 month ago
Nice Simplification.
A word of caution for Method1:
1)How to calculate square of a number close to 50:
Its (50+x)^2=2500+x^2+2*50*x
=(25+x)*100+x^2
So,for this method to work,x^2(-10)<x<10
So this method will work for all squares from 41 to 59.
2)Working for Method2:
x5^2,where as said by Handa,x can be anything,
x5^2=(x*10+5)^2=100x^2+25+100^x
=100x(x+1)+25
which proves what Handa has stated in simple words:)
Once again,the point is working can be understood once,but once attempting question,only the method should be mind:)
about 1 month ago
@Arunim – Thanks for the details.
about 1 day ago
Hey
Nice shortcut and thanks for the logic behind it as well. You guys are geniuses
Please post more shortcuts as and when you find. Thanks
Chinmay