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Squaring theSquaring theSquaring the
NumbersNumbersNumbers
By: Krishna Kumar Kumawat
Maths Teacher
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What is squaring?
Squaringmeans that
multiplying the
term by itself.
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Square of numbers whose unit digit isSquare of numbers whose unit digit is
Zero ( 0 )Zero ( 0 )
Just double the number of zeros at the
right side and write the square of
the non-zero number in left.
Example 1: 40 2= 1600
Example 2: 7002= 490000
Example 3: 21002
= 4410000Example 4: 130002= 169000000
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 5.is 5.
Write 25 in the right most place,
then. Multiply the rest number
with its successive number andwrite in the left
Example 1: 25 2= 625
Example 2: 652= 4225
Example 3: 852= 7225Example 4: 1152= 13225
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 1.is 1.Write the square of the previous
number and then add the
previous number and the numberwhose square is being askedExample 1: 21 2= 202+ (20 + 21)
= 400 + 41
= 441
Example 2: 81
2
= 80
2
+ (80 + 81)= 6400 + 161
= 6561
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 9.is 9.It is very similar to the previous case.
The difference is that here we have
to subtract instead of addition.Example 1: 392= 402 ( 39 + 40 )= 1600 - 79
= 1521
Example 2: 1292= 1302 ( 129 + 130 )
= 16900 - 259
= 16641
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 2.is 2.
Write the square of the base number
and then multiply the sum of
the previous number and thenumber whose square is being
asked, then add.Example 1: 522= 502+ 2( 50 + 52)
= 2500 + 204
= 2704Example 2: 1122= 1102+ 2( 110 + 112)
= 12100 + 44 4
= 12544
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 3.is 3.Write the square of the base number
and then multiply the sum of
the base number and the number
whose square is being asked by 3,
then add it in the square of base
number.Example 1: 23 2= 202+ 3 ( 20 + 23 )
= 400 + 129= 529
Example 1: 532= 502+ 3 ( 50 + 53 )
= 2500 - 309
= 2809
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 7.is 7.Write the square of the base number
and then multiply the sum of
the base number and the number
whose square is being asked by 3,
then subtract it from the square of
base number.Example 1: 472 = 502 - 3 ( 47 + 50 )
= 2500 - 291= 2209
Example 1: 372 = 140 2 - 3 ( 137 + 140 )
= 19600 - 831
= 18769
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 4.is 4.Write the square of the base number
and then subtract the sum of base
number and the number whose
square is being asked from the
square of the base number.
Example 1: 342= 352 ( 34+ 35 )
= 1225 - 69
= 1156Example 2: 542= 552 ( 54 + 55 )
= 3025 - 109
= 2916
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Square of numbers whose unit digitSquare of numbers whose unit digit
is 6.is 6.Write the square of the base number
and then add the base number
and the number whose square is
being asked
Example 1: 362= 352 + (35+ 36)
= 1225 + 71
= 1296
Example 2: 762= 752+ (75 + 76)
= 5625 + 151
= 5776
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Important properties of squaresImportant properties of squares
1. The numbers with unit digit 0 , 1,
5 or 6 always give the same unit
digit respectively, on squaring .
2. If the unit digit of any number is 9
then the unit digit of the square of
its number is always 1.
3. If the unit digit of any number is 2or 8 then the unit digit of the
square of its number is always 4.
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Important properties of squaresImportant properties of squares
4. If the unit digit of any number is 3
or 7then the unit digit of the
square of its number is always 9.
5. If the unit digit of any number is 4
or 6 then the unit digit of the
square of its number is always 6 .
6. 2, 3 7 and 8 never appear at unit
digit in the square of a number.
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Squaring the NumbersSquaring the Numbers
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Prepared by :Krishna Kumar Kumawat
Maths Teacher
C.F.D.A.V. Public School,Gadepan, Kota
Rajasthan
E-mail: [email protected]. 009928407883
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