How to find square roots of numbers without using calculator

Square roots of numbers
Square roots of numbers
Table of square roots
Table of square roots
Table of square roots
Table of square roots
Table of square roots
Table of square roots

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

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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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