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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: kkk992840@yahoo.comMob. 009928407883

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