Solution to Finding Squares of Numbers: Easy Method
Anybody having difficulty with squares and square roots? Your guide awaits.
I don’t particularly enjoy people going against me when I show off, but I have to say I am an absolute topper in my math class. Algebra, easy. Geometry, easy. Fractions, easy. Basic arithmetic, easiest. That’s why today I’m going to help with solving squares of numbers, and this a very easy method. Atleast it’s more easier than multiplying a number with the same number.
Now I myself only know the squares of numbers upto 25 by heart, and I’m only 13 years old. I’m not going to show off and simply dictate it. I’m going to give my method.
Here’s the tip
- Square of 1- 1
- Square of 2- 4
- Square of 3- 9
- Square of 4- 16
- Square of 5- 25
- Square of 6- 36
Take all these numbers into hand, and try to find a pattern. If you can’t find any, here’s a hint: subtraction. Look at the difference of 4 and 1. It’s 3. For 4 and 9? It’s 5. And for 9 and 16, it’s 7. Now, the differences are 3, 5 and 7. If you continue you will get 9, 11, 13, 15 and so on.
Got the tip? It is simply adding two more to the square from the previous square. If you didn’t understand what I just said, here’s how it goes-
Suppose you want the square root of 11. Simply use the method to get it to the square of 10, which is 100. That is, square of 1 plus 3 to get the square of 2, square of 2 plus the previous odd number used+ 2, which is 5, to get 9, which is the square root of 3. This method you can use till however long you please.
Now let’s get back to the sum we want to solve. The square of 11. By following the method, get it to the square of 10, which is 100. Difference between square of 10 and 9, 100-81 which is 19. Now you have the number 19. Add two to that, to get 21. Then you add that number to 100 and you’ll get the square of 11, exactly 121.
Pretty neat isn’t it?
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4 Responses to “Solution to Finding Squares of Numbers: Easy Method”
On September 21, 2009 at 2:10 pm
Yeah this is right ,so basically:
square of 1= 1
square of 2= 1 3
square of 3= 1 3 5
square of 4= 1 3 5 7
square of 5= 1 3 5 7 9 & so on.
There’s an easy & powerful method to find ANY square provided you know to find the square of the nearest number (ending in 5 or 0) to the number required…
for eg: if you know 65 square & 70 square…you can within seconds find out the square of 66,67,68,69..
So first the method to find out squares of numbers ending in 5…(so that it will help to find for eg. 65 square)
SIMPLE: 65 SQUARE IS (6×7(ie. next digit))appended by 25..ie 4225
75 square is 7×8=56 & therefore 5625 !!
175 square is(17×18)25=30625!!
Now moving further , 66 square = 65 square+ 66th odd number. And ‘n’th odd number = 2n-1…therefore 66th odd number is (66×2)-1=131
So 66 square is 4225+131=4356 !!!!!!!
For 69 square , the same thing but subtraction ie. 70 square -69th odd no.That means 4900-(2×70-1)=4900-139=4761 !!!!
For 67 square: 65 square +(sum of 66th &67th odd nos)..this sum ie. bracket one is nothing but 4×66…ie. 4225+(4×66)=4489 !!!!!!!
For 68 square:same thing but subtraction ie. 70 square-(sum of 69th &70th odd nos) ie. 4900-(4×69)=4624 !!!!!!
So in short if we can find quickly the squares of all numbers ending in 5 or 0…which is actually easy to find as i have elaborated earlier, we can find ANY SQUARE quickly !!!!
On September 21, 2009 at 2:35 pm
oh i missed the ‘+’ sign in the table above..it should read:
square of 1= 1
square of 2= 1 + 3
square of 3= 1 + 3 + 5
square of 4= 1 + 3 + 5 + 7
square of 5= 1 + 3 + 5 + 7+ 9 & so on
On October 19, 2009 at 2:27 pm
well how to find the square of 99999989999.
On October 29, 2009 at 6:16 am
by the method of eknyunen purven
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