1 added
92 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>243 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 20.2.</p>
4
-
<h2>What is the Square Root of 20.2?</h2>
5
-
<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 20.2 is not a<a>perfect square</a>. The square root of 20.2 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √20.2, whereas (20.2)^(1/2) in the exponential form. √20.2 ≈ 4.49444, 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 20.2</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 long-<a>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 20.2 by Long Division Method</h2>
12
<p>The<a>long 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<a>square root</a>using the long division method, step by step:</p>
1
<p>The<a>long 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<a>square root</a>using the long division method, step by step:</p>
13
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from the<a>decimal</a>point. In the case of 20.2, consider it as 20.20 and group it as 20 and 20.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from the<a>decimal</a>point. In the case of 20.2, consider it as 20.20 and group it as 20 and 20.</p>
14
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 20. We can say n is ‘4’ because 4 x 4 = 16, which is less than or equal to 20. Now the<a>quotient</a>is 4; after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 20. We can say n is ‘4’ because 4 x 4 = 16, which is less than or equal to 20. Now the<a>quotient</a>is 4; after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
15
<p><strong>Step 3:</strong>Bring down 20, making the new<a>dividend</a>420. Add the old divisor (4) with itself, giving us 8, which will be our new divisor prefix.</p>
4
<p><strong>Step 3:</strong>Bring down 20, making the new<a>dividend</a>420. Add the old divisor (4) with itself, giving us 8, which will be our new divisor prefix.</p>
16
<p><strong>Step 4:</strong>Find a digit (x) such that 8x multiplied by x is less than or equal to 420. The number 84 fits because 84 x 4 = 336.</p>
5
<p><strong>Step 4:</strong>Find a digit (x) such that 8x multiplied by x is less than or equal to 420. The number 84 fits because 84 x 4 = 336.</p>
17
<p><strong>Step 5:</strong>Subtract 336 from 420, resulting in a remainder of 84. The quotient so far is 4.4.</p>
6
<p><strong>Step 5:</strong>Subtract 336 from 420, resulting in a remainder of 84. The quotient so far is 4.4.</p>
18
<p><strong>Step 6:</strong>Add a decimal point and two zeros to the remainder to continue. Now the new dividend is 8400.</p>
7
<p><strong>Step 6:</strong>Add a decimal point and two zeros to the remainder to continue. Now the new dividend is 8400.</p>
19
<p><strong>Step 7:</strong>Repeat the process to find the next digit of the quotient, which will be 9 since 849 x 9 = 7641.</p>
8
<p><strong>Step 7:</strong>Repeat the process to find the next digit of the quotient, which will be 9 since 849 x 9 = 7641.</p>
20
<p><strong>Step 8:</strong>Subtract 7641 from 8400, giving a remainder of 759.</p>
9
<p><strong>Step 8:</strong>Subtract 7641 from 8400, giving a remainder of 759.</p>
21
<p><strong>Step 9:</strong>Continuing this process will yield a more precise square root.</p>
10
<p><strong>Step 9:</strong>Continuing this process will yield a more precise square root.</p>
22
<p>The square root of √20.2 is approximately 4.494.</p>
11
<p>The square root of √20.2 is approximately 4.494.</p>
23
-
<h3>Explore Our Programs</h3>
12
+
24
-
<p>No Courses Available</p>
25
-
<h2>Square Root of 20.2 by Approximation Method</h2>
26
-
<p>The approximation method is another method for finding square roots; 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 20.2 using the approximation method.</p>
27
-
<p><strong>Step 1:</strong>Identify the closest perfect squares around 20.2.</p>
28
-
<p>The smallest perfect square less than 20.2 is 16, and the largest perfect square more than 20.2 is 25.</p>
29
-
<p>Therefore, √20.2 falls between 4 and 5.</p>
30
-
<p><strong>Step 2:</strong>Apply the linear approximation<a>formula</a>:</p>
31
-
<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
32
-
<p>Using this, (20.2 - 16) / (25 - 16) = 4.2 / 9 ≈ 0.4667.</p>
33
-
<p>Now add this decimal to the lower bound (4): 4 + 0.4667 ≈ 4.47.</p>
34
-
<p>Thus, the approximate square root of 20.2 is about 4.47.</p>
35
-
<h2>Common Mistakes and How to Avoid Them in the Square Root of 20.2</h2>
36
-
<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. 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 √19?</p>
39
-
<p>Okay, lets begin</p>
40
-
<p>The area of the square is 19 square units.</p>
41
-
<h3>Explanation</h3>
42
-
<p>The area of the square = side².</p>
43
-
<p>The side length is given as √19.</p>
44
-
<p>Area of the square = side² = √19 x √19 = 19.</p>
45
-
<p>Therefore, the area of the square box is 19 square units.</p>
46
-
<p>Well explained 👍</p>
47
-
<h3>Problem 2</h3>
48
-
<p>A square-shaped building measuring 20.2 square feet is built; if each of the sides is √20.2, what will be the square feet of half of the building?</p>
49
-
<p>Okay, lets begin</p>
50
-
<p>10.1 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 20.2 by 2 = we get 10.1.</p>
54
-
<p>So half of the building measures 10.1 square feet.</p>
55
-
<p>Well explained 👍</p>
56
-
<h3>Problem 3</h3>
57
-
<p>Calculate √20.2 x 3.</p>
58
-
<p>Okay, lets begin</p>
59
-
<p>13.4832</p>
60
-
<h3>Explanation</h3>
61
-
<p>The first step is to find the square root of 20.2, which is approximately 4.494.</p>
62
-
<p>The second step is to multiply 4.494 by 3.</p>
63
-
<p>So 4.494 x 3 ≈ 13.4832.</p>
64
-
<p>Well explained 👍</p>
65
-
<h3>Problem 4</h3>
66
-
<p>What will be the square root of (16 + 4.2)?</p>
67
-
<p>Okay, lets begin</p>
68
-
<p>The square root is approximately 4.494</p>
69
-
<h3>Explanation</h3>
70
-
<p>To find the square root, we need to find the sum of (16 + 4.2). 16 + 4.2 = 20.2, and then √20.2 ≈ 4.494.</p>
71
-
<p>Therefore, the square root of (16 + 4.2) is approximately ±4.494.</p>
72
-
<p>Well explained 👍</p>
73
-
<h3>Problem 5</h3>
74
-
<p>Find the perimeter of the rectangle if its length ‘l’ is √19 units and the width ‘w’ is 5 units.</p>
75
-
<p>Okay, lets begin</p>
76
-
<p>We find the perimeter of the rectangle as approximately 28.72 units.</p>
77
-
<h3>Explanation</h3>
78
-
<p>Perimeter of the rectangle = 2 × (length + width).</p>
79
-
<p>Perimeter = 2 × (√19 + 5) = 2 × (4.359 + 5) = 2 × 9.359 ≈ 18.72 units.</p>
80
-
<p>Well explained 👍</p>
81
-
<h2>FAQ on Square Root of 20.2</h2>
82
-
<h3>1.What is √20.2 in its simplest form?</h3>
83
-
<p>The simplest form of √20.2 is √20.2, as it cannot be simplified further into a<a>product</a>of integers.</p>
84
-
<h3>2.Mention the factors of 20.2.</h3>
85
-
<p>Factors of 20.2 are 1, 2.02, 10.1, and 20.2.</p>
86
-
<h3>3.Calculate the square of 20.2.</h3>
87
-
<p>We get the square of 20.2 by multiplying the number by itself, that is 20.2 x 20.2 = 408.04.</p>
88
-
<h3>4.Is 20.2 a prime number?</h3>
89
-
<h3>5.20.2 is divisible by?</h3>
90
-
<p>20.2 is divisible by 1, 2.02, 10.1, and 20.2.</p>
91
-
<h2>Important Glossaries for the Square Root of 20.2</h2>
92
-
<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>
93
-
<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>
94
-
<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>
95
-
<li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals. </li>
96
-
<li><strong>Linear approximation:</strong>A method to estimate the value of a function close to a known value, often used to approximate square roots by finding the nearest perfect squares.</li>
97
-
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
98
-
<p>▶</p>
99
-
<h2>Jaskaran Singh Saluja</h2>
100
-
<h3>About the Author</h3>
101
-
<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>
102
-
<h3>Fun Fact</h3>
103
-
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>