How to find Squares of any numerals without using calculator: squares of numbers

The squares of numbers are gotten when the number is multiplied by itself. When T is multiplied by T, that is T x T, it is being written as T² in a short form.

Some examples of Squares are:

0.3² = 0.3 x 0.3 = 0.09
2.5² = 2.5 x 2.5 = 6.25
7² = 7 x 7 = 49
0.5² = 0.5 x 0.5 = 0.25

Table of Squares of numbers

This is a table used to find the squares of numerals without using calculator. It is being used exactly the way they use logarithms table.

Both Decimal and whole numerals have their squares in the table but the position of the decimal point must be located carefully.

HOW TO USE TABLE OF SQUARES (squares of numbers):

If for instance you are told to find the Square of 3.677.

First thing to do here is to open your four figure table and locate where SQUARES OF NUMBERS is written.

Second step: Study the table and you will notice that it has two major columns, with the first having sub-columns running from Zero to Nine and the second from One to Nine which is the DIFFERENCE side.

Third step is to divide the figure (3.677) into three parts allowing only the very first part to have two digits and the rest one digit each. 36 -7 -7

Fourth step: look for 36 on the first column “under” 7 difference 7.

36 under 7 in the four figure table = 1347

Difference 7 = 5

Fifth step is to add up 1347 and 5 = 1352

Six step is how to place the decimal. Observe that the square of 3.677 will definitely lie between the square of 3 and 4.

3.677² lies between 3² and 4² which is between 9 and 16.

Therefore 3.677² = 13.52

QUESTIONS AND SOLUTIONS: (squares of numbers)

From the table of squares, find the squares of the following figures.

Q1: 23

Look for 23 under zero(0).

23 under zero = 5290

It lies between 23² and 24² which is between 529 and 576

So, 23² = 529

Q2: 6.91

Look for 69 under 1

69 under 1 = 4775
Now, the placement of the decimal is crucial.

The answer will fall between 6² and 7² which is 36 and 49 = 47.75

Q3: 29.41

Look for 29 under 4 and difference 1

29 under 4 = 8644
Difference 1 = 6

Add the two = 8644 + 6 = 8650

It lies between 29² and 30² which is between 841 and 900

Thus, 29.41² = 865

Q4: 9.463

Look for 94 under 6, difference 3.

94 under 6 = 8949
Difference 3 = 6

Add the two 8949 + 6 = 8955

The answer lies between 9² and 10² which is between 81 and 100
= 89.55

Q5: 264

Look for 26 under 4

26 under 4 = 6970

It lies between 26² and 27² that is between 676 and 729

Hence, 264² = 69696

Q6: 2.007

Search for 20 under 0, difference 7

20 under 0 = 4000
Difference 7 = 29

Add 4000 + 29 = 4029

The answer will be between 2² and 3² that is between 4 and 9 = 4.029

Q7: 0.5413

Search 54 under 1, difference 3

54 under 1 = 2927
Difference 3 = 3

Add the two = 2930

It falls between 0.5² and 0.6² that is between 0.25 and 0.36 = 0.293

Q8: 0.0674

Look for 67 under 4

67 under 4 = 4543
The answer falls between 0.06² and 0.07² that is between 0.0036 and 0.0049
= 0.004543

Q9: 0.069

Look for 69 under 0
= 4761

It lies between 0.06² and 0.07² that is between 0.0036 and 0.0049
= 0.004761

Q10: 3.461

Look for 34 under 6, difference 1

34 under 6 = 1197
Difference 1 = 1
Add the two = 1198

The answer lies between 3² and 4² that is between 9 and 16.
= 11.98

Q11: 42.13

Search for 42 under 1, difference 3

42 under 1 = 1772
Difference 3 = 3
Add both = 1775

It lies between 42² and 43² which is between 1764 and 1849
= 1775

Q12: 76.34

Search for 76 under 3, difference 4

76 under 3 = 5822
Difference 4 = 6
Add both = 5828

It lies between 76² and 77² that is 5776 and 5929
Therefore 76.34² = 5828

Q13: 0.5147

Look for 51 under 4, difference 7

51 under 4 = 2642
difference 7 = 7
Add the two = 2649

It lies between 0.5² and 0.6² which is between 0.25 and 0.36 = 0.2649

Q14: 89.24

Look for 89 under 2, difference 4

89 under 2 = 7957
difference 4 = 7
Add the both = 7964

The answer lies between 89² and 90² that is between 7921 and 8100
= 7964

Q15: 16.4

Check 16 under 4

16 under 4 = 2690
The answer lies between 16² and 17² which is between 256 and 289
= 269

Q16: 0.0024

Look for 24 under 0

24 under 0 = 5760
The answer lies between 0.002² and 0.003² that is between 0.000004 and 0.000009
= 0.00000576

Q17: 0.1006

10 under 0 = 1000
Difference 6 = 13

Add up = 1013

It lies between 0.1² and 0.2² that is between 0.01 and 0.04 = 0.01013

Q18: 0.0008

80 under 0 = 6400

It lies between 0.0008² and 0.0009² that is between 0.00000064 and 0.00000081 = 0.00000064

Q19: 0.0246

24 under 6 = 6052

The answer lies between 0.02² and 0.03² which is between 0.0004 and 0.0009
= 0.0006052

Q20: 11.62

11 under 6 = 1346
Difference 2 = 5
Add up = 1351

The answer lies between 11² and 12² which is between 121 and 144
= 135.1

Click here to see Mathematics past questions and answers on

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