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.

Hence:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

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 chibase.com.ng

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