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
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