Square Of a Number Between 100 and 200

It is long time since I have written any posts. I was little busy training some students Vedic Maths. Then there was a IWA ’umang’ mela which I had participated, so designing brochure and printing took some time. No more excuses, let us start learning ahead.

We have seen in the post Square of a number – Part 1 how to find square of numbers from 11-20, square of numbers ending with 5, square of number next to well-known number. Let us learn how to find square of a number between 100 and 200

First thing to remember is square of any number between 100 and 199 is five digits.
Step1: The last two digits of the square of the number are the square of the last two digits. (If there is any carry keep it aside)
Step2: The first three digits of the square of the number are the number plus the last two digits of the square plus the carry from Step1.
Step3: Answer= Step2| Step1

Let us take two examples to explain these steps.

Example1: (102)²
Step1: Last two digits= Square of last two digits (02)²= 04
Step2: First three digits= Number (102) + last two digits (02) + carry (0)
= 102+ 02+ 0= 104
Step3: Answer= Step2| Step1= 10404

Finding this sum easy to do, let us take one more example.

Example2: (159)²
Step1: Last two digits, Square of last two digits (59)
we learned this in the Square of number Part 1
= 60² ₋ (60+ 59)= 3600  119= 3481, carry= 34 last two digits= 81

Step2: First three digits= Number (159) + last two digits (59) + carry (34)
= 159+ 59 + 34 (check post on easy addition)
= 252

Step3: Answer= Step2| Step1= 25281
I am sure you have understood how to find square of number between 100 and 199.

Practice:
1) 124²
2) 176²
3) 189²
4) 108²
5) 171²

Formula to Find square of a number
We have seen how to find square of numbers ending with 5 e.g. 25², 35² etc., finding squares of number ending with zero is easy e.g. 40², 70² etc., we have learned how to find squares of the numbers adjacent to the well know numbers e.g.21², 24², 26², 29² between 20 and 30, but what about numbers like 22, 23, 26, 27? How to find squares of these numbers?
To get square of any number we can use the formula.
Let us take a number x which we can write  in the form a+ b where a and b are numbers whose squares are easy to find.
Then x²= (a+ b)² =a²+ 2× a× b+ b²

Let us take an example 37² =?
37²= (30+ 7)²= 30²+ 2× 30× 7+ 7²
= 900+ 420+ 49
Ans. = 1369

Let us take one more example 123²=?
123 = 120+ 3 or 99+ 24 we will take 120+ 3
123²= (120+ 3)²= 120²+ 2× 120× 3+ 3²
= 14400+ 720+ 9
Ans. = 15129

Let us take another number y which we can write in the form m− n where m and n are numbers whose squares are easy to find.
Then y²= (m-n)²= m²- 2× m× n + n²

Let us take an example 87²=?
87²= (90− 3)²= 90² −2×90×3+ 3²
= 8100− 540+ 9
= 7569

Practice:
1) 67²
2) 73²
3) 127²
4)147²
5) 132²
6) 82²
7) 42²
8)112²