Dear Aspirants,
Today we will learn squaring of 2-digit and the 3-digit number, in competitive exams where time management is very important, the easy square trick is essential, So there is a Vedic method and some other tips & tricks for squaring, in this method the more you practice then you will take less time for doing square. So Let's start...
Squaring of 2-Digit Number
For squaring any two-digit number there is a universal method called the Urdhvatiryak method. this method is easy to calculate and less time-consuming Let's take an easy example
Ex. 1) Square of 17 = (17)²
Step 1: you have to write in the below format
1 7
1 7
---------
Step 2: Now you have to write like below
1 1 7 7
1 1 7 7
---- ------- ----
Step 3: Now next step is some kind of solution
Step 4: After the above arrangement multiplies 1×1 then (1×7 + 1×7) = 14 and 7×7. After that write like below.
Step 5: Always write in two-digit numbers like 1 to 01. After that, there is an addition method.
Now understand what happens above, Starting from the right-hand side the unit digit of 49 number 9 is directly placed, after that tens no. 4 is added with next no. 14 which will give 18 and unit digit no. 8 is below written, after that again unit digit no. 1 is added with next no. 1 and resultant give 2.
So, the answer is (17)² = 289
Now let's take a hard example
Ex. 2) Square of 89 = (89)²
Step 1: Write in the below format
8 8 9 9
8 8 9 9
---- --------- ----
Step 2:
Left side Middle Part Right side
(8 × 8) = (9×8 + 9×8) = (9×9) =
64 72+72 = 81
144
Step 3:
Starting from the right-hand side the unit digit of 81 number is 1 and directly placed below, after that tens no. 8 is added with next no. 144 which will give 152 and unit digit 2 is written below after that 15 is added to the left-hand side number 64 and gives the resultant 79.
So, the Square of 89 is 7921.
After practising more on this method you take less time to solve and you only write numbers and solve directly like the below example
Ex. 3) (64)²
Solution:
Square Trick of a number in which the last digit is 5
There is a shortcut trick for a number whose last digit or unit digit is 5.
let's understand with a little formula
Suppose the number is X5, so the square of X5 is (X5)²
we all know 5² = 25 the unit digits or right-hand side digit is always 25
X 5²
↓ ↓
X(X+1) 25
Let's understand by example
Ex. 4) (35)² where X is 3 in this case so by the formula
3 5
↓ ↓
3×(3+1) 5 ²
3×4 ↓
12 25
so (35)² = 1225
Ex. 5 & 6)
In example 5 the square of 65, the unit digit is the 25 after that number 6 is multiplied by the next number which is 7 means 6×7 = 42 also similarly applied for example 6.
This method also works in three-digit square numbers whose unit digit is 5
Ex. 7) Square of 115
11 5
↓ ↓
11×(11+1) 5²
11×12 ↓
132 25
so (115)² = 13225
Let's take a hard example
Ex. 8) Square of 785
6162 25
so (785)² = 616225
Square Trick of numbers between 90 & 100
If you have to find a square number between 90 and 99 there is a trick.
If we have to find (97)²
In number 97 we will take the difference from 100 which will give 3 = (100 - 97). So doing the square of 3 which is 9 but we write in two-digit number 09 and after that, we have to do 97 - 3 = 94 which gives the answer 9409. Let's understand step by step.
Ex. 9) (97)²
Step 1: 100 - 97 = 03 | (3)² = 09
Step 2: 97 - 3 = 94
Step 3: Answer 9409
Ex. 10)
Note: Always remember the above method only use numbers between 90 to 100.
Square Trick of numbers between 100 & 110
If you have to find a square number between 100 and 110 the trick is the same as the above trick but with a little twist in it.
If we have to find (103)²
In number 103 we will add the number which will be more than 100 which will give 3 = (103 -100). So doing the square of 3 which is 9 but we write in two-digit number 09 and after that, we have to do 103 + 3 = 106 which gives the answer 10609. Let's understand this step by step.
Ex. 11) (103)²
Step 1: 103 = 100 + 03 = 03 | (3)² = 09
Step 2: 103 + 3 = 106
Step 3: Answer 10609
Ex. 12) (107)²
Step 1: 107 = 100 + 7 = 07 | (7)² = 49 (Right hand side digits)
Step 2: 107 + 7 = 114 (Left hand side digits)
arrange all in sequence
Step 3: Answer 11449
Squaring of 3-Digit Number
Squaring any 3-digit number is also done by the Vedic Urdhvatiryak method. The main concept is like 2 digits squaring method but little a few changes in it. Let's understand by the examples
Ex. 13) Square of 168 = (168)²
Step 1: Arrange it as shown below
1 1 6 1 6 8 6 8 8
1 1 6 1 6 8 6 8 8
--- ---- -------- ----- ---
Step 2: In the next step do some calculations as given below, as shown in the diagram the arrow shows the multiplication of numbers.
Step 3:
Step 4: Now add those numbers like the above method which you know in the above examples.
So (168)² = 28224
Ex. 14) Find (843)²
After practising more you can directly solve this within seconds as given below.
So, (843)² = 710649.
For more information on this and want to command more in the above 3-digit multiplication method read this article Easy 3 Digit Multiplication Trick for Competitive Exams - Vedic Method
I hope you understand this method, If you have any doubt feel free to comment.
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Your Gyaan INside
