How to Use a Table to Find Square Roots

Oct 13, 2025 by miodeya.com 11 views

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Introduction

In mathematics, finding the square root of a number is an essential operation that has numerous applications in various fields, including algebra, geometry, and trigonometry. The square root of a number is a value that, when multiplied by itself, gives the original number. In this article, we will explore how to find the square root of a number using a table, with a focus on finding the square root of 689.341.

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. Similarly, the square root of 25 is 5, because 5 multiplied by 5 equals 25.

Why Use a Table to Find Square Roots?

Using a table to find square roots can be a quick and efficient way to calculate square roots, especially for large numbers. A table of square roots can be used to look up the square root of a number, rather than having to calculate it manually.

How to Use a Table to Find Square Roots

To use a table to find the square root of a number, follow these steps:

Locate the number: Find the number for which you want to find the square root in the table.
Read the square root: The square root of the number is listed in the table.
Check the accuracy: Double-check the accuracy of the square root by multiplying it by itself to ensure that it equals the original number.

Finding the Square Root of 689.341

To find the square root of 689.341 using a table, follow these steps:

Locate the number: Find the number 689.341 in the table.
Read the square root: The square root of 689.341 is listed in the table as approximately 26.24.
Check the accuracy: Multiply 26.24 by itself to ensure that it equals 689.341.

Calculating the Square Root Manually

If you don't have access to a table of square roots, you can calculate the square root manually using the following formula:

√x = √(a^2 + b^2)

where x is the number for which you want to find the square root, and a and b are the two numbers that, when squared and added together, equal x.

For example, to find the square root of 689.341 manually, you can use the following formula:

√689.341 = √(26^2 + 0.24^2)

Using a Calculator to Find Square Roots

If you have a calculator, you can use it to find the square root of a number quickly and easily. Simply enter the number for which you want to find the square root, and the calculator will display the square root.

Conclusion

Finding the square root of a number is an essential operation in mathematics that has numerous applications in various fields. Using a table to find square roots can be a quick and efficient way to calculate square roots, especially for large numbers. In this article, we explored how to find the square root of a number using a table, with a focus on finding the square root of 689.341.

Table of Square Roots

Number	Square Root
1	1
4	2
9	3
16	4
25	5
36	6
49	7
64	8
81	9
100	10
121	11
144	12
169	13
196	14
225	15
256	16
289	17
324	18
361	19
400	20
441	21
484	22
529	23
576	24
625	25
676	26
729	27
784	28
841	29
900	30
961	31
1024	32
1089	33
1156	34
1225	35
1296	36
1369	37
1444	38
1521	39
1600	40
1681	41
1764	42
1849	43
1936	44
2025	45
2116	46
2209	47
2304	48
2401	49
2500	50
2601	51
2704	52
2809	53
2916	54
3025	55
3136	56
3249	57
3364	58
3481	59
3600	60
3721	61
3844	62
3969	63
4096	64
4225	65
4356	66
4489	67
4624	68
4761	69
4900	70
5041	71
5184	72
5329	73
5476	74
5625	75
5776	76
5929	77
6084	78
6241	79
6400	80
6561	81
6724	82
6889	83
7056	84
7225	85
7396	86
7569	87
7744	88
7921	89
8100	90
8281	91
8464	92
8649	93
8836	94
9025	95
9216	96
9409	97
9604	98
9801	99
10000	100

Finding the Square Root of 689.341

To find the square root of 689.341 using the table, locate the number 689.341 in the table and read the square root, which is approximately 26.24.

Checking the Accuracy

To check the accuracy of the square root, multiply 26.24 by itself to ensure that it equals 689.341.

Conclusion

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Q: What is a square root?

A: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

Q: Why is finding the square root of a number important?

A: Finding the square root of a number is important in various fields, including algebra, geometry, and trigonometry. It is also used in real-world applications, such as calculating distances, areas, and volumes.

Q: How do I find the square root of a number using a table?

A: To find the square root of a number using a table, locate the number in the table and read the square root. Make sure to check the accuracy of the square root by multiplying it by itself to ensure that it equals the original number.

Q: Can I use a calculator to find the square root of a number?

A: Yes, you can use a calculator to find the square root of a number quickly and easily. Simply enter the number for which you want to find the square root, and the calculator will display the square root.

Q: How do I calculate the square root of a number manually?

A: To calculate the square root of a number manually, use the following formula:

√x = √(a^2 + b^2)

where x is the number for which you want to find the square root, and a and b are the two numbers that, when squared and added together, equal x.

Q: What is the difference between a square root and a square?

A: A square root and a square are related but distinct concepts. A square root of a number is a value that, when multiplied by itself, gives the original number. A square of a number is the result of multiplying the number by itself.

Q: Can I find the square root of a negative number?

A: No, you cannot find the square root of a negative number in the real number system. However, in complex numbers, the square root of a negative number can be expressed as a complex number.

Q: How do I find the square root of a decimal number?

A: To find the square root of a decimal number, use a calculator or a table of square roots. You can also use the formula:

√x = √(a^2 + b^2)

where x is the decimal number for which you want to find the square root, and a and b are the two numbers that, when squared and added together, equal x.

Q: Can I find the square root of a fraction?

A: Yes, you can find the square root of a fraction by using a calculator or a table of square roots. You can also use the formula:

√x = √(a^2 + b^2)

where x is the fraction for which you want to find the square root, and a and b are the two numbers that, when squared and added together, equal x.

Q: How do I find the square root of a large number?

A: To find the square root of a large number, use a calculator or a table of square roots. You can also use the formula:

√x = √(a^2 + b^2)

where x is the large number for which you want to find the square root, and a and b are the two numbers that, when squared and added together, equal x.

Q: Can I find the square root of a number that is not a perfect square?

A: Yes, you can find the square root of a number that is not a perfect square using a calculator or a table of square roots. You can also use the formula:

√x = √(a^2 + b^2)

where x is the number for which you want to find the square root, and a and b are the two numbers that, when squared and added together, equal x.

Q: How do I check the accuracy of the square root?

A: To check the accuracy of the square root, multiply the square root by itself to ensure that it equals the original number.

Q: Can I use a spreadsheet to find the square root of a number?

A: Yes, you can use a spreadsheet to find the square root of a number. Simply enter the number for which you want to find the square root, and the spreadsheet will display the square root.

Q: How do I find the square root of a number in a programming language?

A: To find the square root of a number in a programming language, use the sqrt() function. For example, in Python, you can use the following code:

import math

x = 16 sqrt_x = math.sqrt(x)

print(sqrt_x)

This will output the square root of 16, which is 4.