To square numbers
close to the bases of powers of 10 i.e. 10, 100, 1000 and so on easily at
extremely fast speed, just follow the steps below:

Step-1: Find the surplus or deficit from the base 10, 100, 1000 & so on

Step-2: Add the surplus (if it is more than base) with or subtract the deficit (if it is less than base) from the whole number given and put the result.

Step-3: Find the square of surplus or deficit and write the result in the last places. Be sure that, since 10 has 1 zero so, 1 more digit to go for numbers near 10, since 100 has 2 zeros so, 2 more digits to go for numbers near 100, accordingly since 1000 has 3 zeros, 3 more digits to go for numbers near 1000 and so on. So, carry forward or put extra zero(s) if necessary to place the digits accurate.

**Squaring numbers close to base 10**

What is the square of
17? or,

**17**^{2}=?
Notice that 17 is
close to base 10. So,

1) Find
the surplus or deficit from base 10. It is 7 surpluses.

2) Since
17 is 7 more than base 10 so, add 7 to the entire number, which is 17+7=24.
Write 24 as the first part of the answer.

3) Now,
since 10 has 1 zero so, 1 more digit to go. Find the square of surplus 7 which
is 49. Write 9 and carry forward 4 to be added to 4 making it 8.

**Squaring numbers close to base 100**

Ideal for squaring
numbers from 76 – 125 (ranges vary at capacity).

**104**

^{2}=?
Notice that 104 is
close to base 100. So,

1) Find
the surplus or deficit from base 100. It is 4 surpluses (104–100=4).

2) Since
104 is 4 more than base 100 so, add 4 to the entire number, which is 104+4 =
108. Write

**108**as the first part of the answer.
3) Now,
since 100 has 2 zeros so, 2 more digits to go. Find the square of surplus 4
which is 16. Write

**16**as the last 2 digits of the answer.So, our answer is

**10816**

Now what if the number that you are trying to square is below the base that is below 100?

Once again, the same thing. Let’s say you want to find

**97**

^{2}
1) Find
the surplus or deficit from base 100. It is (100 – 97 =) 3 less than 100.

2) Since
97 is 3 less than base 100 so, deduct 3 from the entire number, which is 97-3 =
94. Write

**94**as the first part of the answer.
3) Now,
2 more digits to go. Find the square of deficit 3 which is 9. Put

**09**as the last 2 digits of the answer. Notice the extra ‘0’. An extra 0 is to be added to make it a 2 digit number.So, our final answer is

**9409**

**107**

^{2}=?Add the distance (7) from the base 100 to the entire number. 7 + 107 = 114.

Now, 2 more digits to
go. Square of 7 is 49.

So, the answer is 11449.

**113**

^{2}=?
Once again, add
surplus 13 that is the distance from the base 100 to the entire number 113.

So, 113+13 = 126.

Now for the last 2
digits you need to find the square of the distance that is 13.

Square of 13 is 169.

Now put

**69**and add 1 to 126 as we have left 2 places to go to complete the square.
1+126 =

**127**
The answer is

**12769**.**89**

^{2}=?
89 is 11 less than
the base 100.

Subtract 11 from 89,
which is 78.

Square of 11 is 121.

Write 21 in the last
2 places and add 1 to 78 to make

**79**
So, the answer would
be

**7921**.
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