Table of square roots are two types, to estimate a square root of a number from the four figure table is more difficult than doing same in the table of Squares.
The two types of Tables of SQUARE ROOTS are:
1). Square root of numbers between 1 and 10
2). Square root of numbers between 10 and 100
Step by step to find a square root of a number without using calculator.
If a number 78259 is given to find its square root, the first thing to do is to mark off the given number in pairs of digits starting from the decimal point, mark both to the left and to the right;
Note: 78259 = 78259.0
So marking the number in pairs of digits starting from the decimal point;
To the left = 7, 82, 59
To the right = 0
Hope you noticed that we marked it in pairs from the left to the right leaving a remainder of one digit (7) that is not paired.
Step two is to note down the compartment after marking the given number in pairs of digits which is three(3), that is 7 = 1, 82 = 2, 59 = 3 compartments.
From the pairing of the digits, you can see that 7 is standing alone which means that the square root table that will be checked must be the one between 1 and 10.
Step three is to look for 7.8 under 2 and difference 6
7.8 under 2 = 2.796
Difference 6 = 1
Step four:
Ignore the decimal point and add both; 2796 + 1 = 2797
Step five:
Recall that the given number has three compartments in the pairing of digits we did earlier.
Thus, the answer is 279.7
Example 2:
Find the square root of 0.00068310
Solution:
Marking off the given number in pairs of digits starting from the decimal point, mark both to the left and to the right.
To the right = 0. 00, 06, 83, 1
To the left = 0
Note that moving to the left gives only zero = Zero and moving to the right, we see another zero in pairs which is also = Zero(one zero), 06, 83, 1
Noting down the compartment after marking the given number in pairs of digits which is five(5)
Check 6.8 under 3 and difference 1
6.8 under 3 = 2.613
Difference 1 = 0
Ignore the decimal point and add both; 2613 + 0 = 2613
Recall that the compartment we have here is five; that is “Zero” going to the left, Zero-Zero” going to the right, “Zero-six” going to the right, Eight-Three and “One” going to the right.
The answer is now 0.02613
Example 3:
Find the square root of 8.742
Solution:
√8.742 lies between √4 and √9
Marking off to the left = 8
To the right = 74, 2
The square root will be found on the square root of numbers between 1 and 10
Look for 8.7 under 4 and difference 2
8.7 under 4 = 2.956
Difference 2 = 0
Add the both without the decimal = 2956
Answer = 2.956
Example 4:
Find the square root of 87.42
Solution:
√87.42 lies between √81 and √100 which is 9 nd 10
It will be checked under the squares of numbers between 10 and 100
Marking it off to the left = 87
Marking off to the right = 42
It has two compartments
Look for 87 under 4 and difference 2
87 under 4 = 9349
Difference 2 = 1
Add them = 9349 + 1 = 9350 = 935
Since the √87.42 lies between 9 and 10, the answer is 9.35
QUESTIONS and SOLUTIONS:
Use tables of Square roots to find the square roots of these numbers.
Q1. 2694
Solution:
Pair the digits from the decimal point to the left = 26, 94
It will be checked on a square root of numbers between 10 and 100
Look for 26 under 9 and difference 4pp
26 under 9 = 5187
Difference 4 = 4
5187 + 4 = 5191
= 51.91
Q2: 8.721
Solution:
Pairing to the right = 72, 1
Pairing to the left = 8
√8.721 lies between √4 and √9, that is between 2 and 3
It will be checked between 1 to 10 on the four figure table.
Look for 8.7 under 2 and difference 1
8.7 under 2 = 2953
Difference 1 = 0
= 2953
Since the square root of 8.721 lies between 2 and 3, the answer is now = 2.953
Q3: 0.0236
Solution:
From left to right = 02, 36
From right to left = 0
Look for 2.3 under 6 = 1536
Answer = 0.1536
Q4: 0.000072
Solution:
Pairing to the right = 00, 00, 72
To the left = 0
Look for 72 under 0
72 under 0 = 8485
= 0.008485
Q5: 36.58
Solution:
Pairing from right = 36
From left = 58
√36.58 lies between √36 and √49 which is between 6 and 7
Look 36 under 5 and difference 8
36 under 5 = 6042
Difference 8 = 7
Add the two = 6049
The square lies between 6 and 7, that means the answer is 6.049
Q6: 356
Solution:
To the left = 3, 56
Look for 3.5 under 6 = 1887
It has two compartments, so the answer = 18.87
Q7: 16
Solution:
To the left = 16
It has one compartment
Look for 16 under 0 = 4.000
Q8: 42.13
Solution:
To the left = 42
To the right = 13
The square root of 42.13 will lie between √36 and √49 which is 6 and 7
Look for 42 under 1 and difference 3
42 under 1 = 6488
Difference 3 = 2
= 6490
Answer = 6.49
Q9: 29.41
Solution:
To the left = 29
To the right = 41
The square root of 29.41 lies between √25 and √36 which is between 5 and 6
Look for 29 under 4 and difference 1
29 under 4 = 5422
Difference 1 = 1
= 5423 = 5.423
Q10: 16.43
Solution:
Pairing to the right = 43
To the left = 16
The square will lie between √16 and √25 that is between 4 and 5
Check 16 under 4 and difference 3
16 under 4 = 4050
Difference 3 = 4
= 4054 = 4.054
Q11: 0.0024
Solution:
To the right = 00, 24
To the left = 0
Look for 24 under 0 = 4899 = 0.04899
Q12: 24.98
Solution:
The square root will lie between √16 and √25 which is between 4 and 5
To the right = 98
To the left = 24
It has two compartments
Look for 24 under 9 and difference 8
24 under 9 = 4990
Difference 8 = 8
= 4998 = 4.99
Q13: 51.47
Solution:
It lies between √49 and √64, that is between 7 and 8
To the left = 51
To the right = 47
Check 51 under 4 and difference 7
51 under 4 = 7169
Difference 7 = 5
= 7174 = 7.174
Q14: 0.0008
Solution:
To the left = 0
To the right = 00, 08
It has three compartments
Look for 8.0 under 0 = 2828 = 0.02828
Q15: 0.1008
Solution:
To the left = 0
To the right = 10, 08
Look for 10 under 0 and difference 8
10 under 0 = 3162
Difference 8 = 12
= 3174 = 0.31740
Q16: 0.0009009
Solution:
To the left = 0
To the right = 00, 09, 00, 9
Look for 9.0 under 0 and difference 9
9.0 under 0 = 3000
Difference 9 = 1
= 3001 = 0.03001
Q17: 36.71
Solution:
To the left = 36
To the right = 71
√36.72 lies between √36 and √49 which is between 6 and 7
Look for 36 under 7 and difference 2
36 under 7 = 6058
Difference 2 = 2
= 6060 = 6.06
Q18: 274.9
Solution:
Pairing the digits to the left = 2, 74
To the right = 9
Check 2.7 under 4 and difference 9
2.7 under 4 = 1655
Difference 9 = 3
= 1658 = 16.58
Q19: 35.58
Solution:
To the left = 35
To the right = 58
√35 lies between √25 and √36 which is between 5 and 6
Look for 35 under 5 and difference 8
35 under 5 = 5958
Difference 8 = 7
= 5965 = 5.965
Q20: 8.507
Solution:
Pairing the digits From the decimal point to the left = 8
To the right = 50, 7
√8.507 will lie between √4 and √9, which is between 2 and 3 respectively
Check 8.5 under 0 and difference 7
8.5 under 0 = 2915
Difference 7 = 1
Add both of them = 2915 + 1 = 2916
Since the square root of the given number lies between 2 and 3, the answer = 2.916
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