1 added
96 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>175 Learners</p>
2
-
<p>Last updated on<strong>August 5, 2025</strong></p>
3
-
<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 682.</p>
4
-
<h2>What is the Square Root of 682?</h2>
5
-
<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 682 is not a<a>perfect square</a>. The square root of 682 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √682, whereas (682)^(1/2) in exponential form. √682 ≈ 26.0998, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
6
-
<h2>Finding the Square Root of 682</h2>
7
-
<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the<a>long division</a>method and approximation method are used. Let us now learn the following methods:</p>
8
-
<ul><li>Prime factorization method</li>
9
-
<li>Long division method</li>
10
-
<li>Approximation method</li>
11
-
</ul><h2>Square Root of 682 by Prime Factorization Method</h2>
12
-
<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 682 is broken down into its prime factors.</p>
13
-
<p><strong>Step 1:</strong>Finding the prime factors of 682 Breaking it down, we get 2 × 11 × 31.</p>
14
-
<p><strong>Step 2:</strong>Now we found out the prime factors of 682. The second step is to make pairs of those prime factors. Since 682 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
15
-
<p>Therefore, calculating 682 using prime factorization is not straightforward for finding the exact<a>square root</a>.</p>
16
-
<h3>Explore Our Programs</h3>
17
-
<p>No Courses Available</p>
18
-
<h2>Square Root of 682 by Long Division Method</h2>
19
<p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.</p>
1
<p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.</p>
20
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 682, we need to group it as 82 and 6.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 682, we need to group it as 82 and 6.</p>
21
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 6. We can say n is ‘2’ because 2 × 2 = 4 is less than 6. Now the<a>quotient</a>is 2, and after subtracting 4 from 6, the<a>remainder</a>is 2.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 6. We can say n is ‘2’ because 2 × 2 = 4 is less than 6. Now the<a>quotient</a>is 2, and after subtracting 4 from 6, the<a>remainder</a>is 2.</p>
22
<p><strong>Step 3:</strong>Bring down 82, making the new<a>dividend</a>282. Add the old<a>divisor</a>(2) to itself to get 4, which will be part of our new divisor.</p>
4
<p><strong>Step 3:</strong>Bring down 82, making the new<a>dividend</a>282. Add the old<a>divisor</a>(2) to itself to get 4, which will be part of our new divisor.</p>
23
<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n × n ≤ 282. Let n be 6, then 46 × 6 = 276.</p>
5
<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n × n ≤ 282. Let n be 6, then 46 × 6 = 276.</p>
24
<p><strong>Step 5:</strong>Subtract 276 from 282, getting a remainder of 6, and the quotient is 26.</p>
6
<p><strong>Step 5:</strong>Subtract 276 from 282, getting a remainder of 6, and the quotient is 26.</p>
25
<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend, making it 600.</p>
7
<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend, making it 600.</p>
26
<p><strong>Step 7:</strong>The new divisor becomes 52. We find n such that 52n × n ≤ 600. Suppose n is 1, then 521 × 1 = 521.</p>
8
<p><strong>Step 7:</strong>The new divisor becomes 52. We find n such that 52n × n ≤ 600. Suppose n is 1, then 521 × 1 = 521.</p>
27
<p><strong>Step 8:</strong>Subtract 521 from 600, the difference is 79.</p>
9
<p><strong>Step 8:</strong>Subtract 521 from 600, the difference is 79.</p>
28
<p><strong>Step 9:</strong>Continue this process to achieve the desired decimal places.</p>
10
<p><strong>Step 9:</strong>Continue this process to achieve the desired decimal places.</p>
29
<p>So the square root of √682 ≈ 26.0998.</p>
11
<p>So the square root of √682 ≈ 26.0998.</p>
30
-
<h2>Square Root of 682 by Approximation Method</h2>
12
+
31
-
<p>The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 682 using the approximation method.</p>
32
-
<p><strong>Step 1:</strong>Find the closest perfect squares of √682. The closest perfect square less than 682 is 676, and the closest perfect square<a>greater than</a>682 is 729. √682 falls between 26 and 27.</p>
33
-
<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (682 - 676) ÷ (729 - 676) = 6 ÷ 53 ≈ 0.1132 Add this decimal to the lower integer value, 26 + 0.1132 ≈ 26.1132.</p>
34
-
<p>So the square root of 682 is approximately 26.1132.</p>
35
-
<h2>Common Mistakes and How to Avoid Them in the Square Root of 682</h2>
36
-
<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
37
-
<h3>Problem 1</h3>
38
-
<p>Can you help Max find the area of a square box if its side length is given as √682?</p>
39
-
<p>Okay, lets begin</p>
40
-
<p>The area of the square is approximately 465.6404 square units.</p>
41
-
<h3>Explanation</h3>
42
-
<p>The area of the square = side².</p>
43
-
<p>The side length is given as √682.</p>
44
-
<p>Area of the square = side² = √682 × √682 ≈ 26.0998 × 26.0998 ≈ 681.9996</p>
45
-
<p>Therefore, the area of the square box is approximately 682 square units.</p>
46
-
<p>Well explained 👍</p>
47
-
<h3>Problem 2</h3>
48
-
<p>A square-shaped building measuring 682 square feet is built; if each of the sides is √682, what will be the square feet of half of the building?</p>
49
-
<p>Okay, lets begin</p>
50
-
<p>341 square feet</p>
51
-
<h3>Explanation</h3>
52
-
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
53
-
<p>Dividing 682 by 2 = we get 341.</p>
54
-
<p>So half of the building measures 341 square feet.</p>
55
-
<p>Well explained 👍</p>
56
-
<h3>Problem 3</h3>
57
-
<p>Calculate √682 × 5.</p>
58
-
<p>Okay, lets begin</p>
59
-
<p>130.499</p>
60
-
<h3>Explanation</h3>
61
-
<p>The first step is to find the square root of 682, which is approximately 26.0998.</p>
62
-
<p>The second step is to multiply 26.0998 by 5.</p>
63
-
<p>So 26.0998 × 5 ≈ 130.499.</p>
64
-
<p>Well explained 👍</p>
65
-
<h3>Problem 4</h3>
66
-
<p>What will be the square root of (682 + 18)?</p>
67
-
<p>Okay, lets begin</p>
68
-
<p>The square root is 26.</p>
69
-
<h3>Explanation</h3>
70
-
<p>To find the square root, we need to find the sum of (682 + 18).</p>
71
-
<p>682 + 18 = 700, and then √700 ≈ 26.4575.</p>
72
-
<p>Therefore, the square root of (682 + 18) is approximately 26.4575.</p>
73
-
<p>Well explained 👍</p>
74
-
<h3>Problem 5</h3>
75
-
<p>Find the perimeter of the rectangle if its length ‘l’ is √682 units and the width ‘w’ is 38 units.</p>
76
-
<p>Okay, lets begin</p>
77
-
<p>The perimeter of the rectangle is approximately 130.1996 units.</p>
78
-
<h3>Explanation</h3>
79
-
<p>Perimeter of the rectangle = 2 × (length + width).</p>
80
-
<p>Perimeter = 2 × (√682 + 38)</p>
81
-
<p>≈ 2 × (26.0998 + 38)</p>
82
-
<p>≈ 2 × 64.0998</p>
83
-
<p>≈ 128.1996 units.</p>
84
-
<p>Well explained 👍</p>
85
-
<h2>FAQ on Square Root of 682</h2>
86
-
<h3>1.What is √682 in its simplest form?</h3>
87
-
<p>The prime factorization of 682 is 2 × 11 × 31, so the simplest form of √682 remains √682 as it cannot be simplified to a<a>rational number</a>.</p>
88
-
<h3>2.Mention the factors of 682.</h3>
89
-
<p>Factors of 682 are 1, 2, 11, 22, 31, 62, 341, and 682.</p>
90
-
<h3>3.Calculate the square of 682.</h3>
91
-
<p>We get the square of 682 by multiplying the number by itself, that is 682 × 682 = 465124.</p>
92
-
<h3>4.Is 682 a prime number?</h3>
93
-
<h3>5.682 is divisible by?</h3>
94
-
<p>682 has many factors; those are 1, 2, 11, 22, 31, 62, 341, and 682.</p>
95
-
<h2>Important Glossaries for the Square Root of 682</h2>
96
-
<ul><li><strong>Square root</strong>: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4. </li>
97
-
<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>
98
-
<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root. </li>
99
-
<li><strong>Prime factorization:</strong>Expressing a number as the product of its prime factors is prime factorization. </li>
100
-
<li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares by dividing and averaging over several steps.</li>
101
-
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
102
-
<p>▶</p>
103
-
<h2>Jaskaran Singh Saluja</h2>
104
-
<h3>About the Author</h3>
105
-
<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
106
-
<h3>Fun Fact</h3>
107
-
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>