1 added
2 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>286 Learners</p>
1
+
<p>317 Learners</p>
2
<p>Last updated on<strong>August 5, 2025</strong></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 4.2.</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 4.2.</p>
4
<h2>What is the Square Root of 4.2?</h2>
4
<h2>What is the Square Root of 4.2?</h2>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4.2 is not a<a>perfect square</a>. The square root of 4.2 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4.2, whereas (4.2)^(1/2) in the exponential form. √4.2 ≈ 2.04939, 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>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4.2 is not a<a>perfect square</a>. The square root of 4.2 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4.2, whereas (4.2)^(1/2) in the exponential form. √4.2 ≈ 2.04939, 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 4.2</h2>
6
<h2>Finding the Square Root of 4.2</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 the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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 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>
8
<ul><li>Prime factorization method</li>
9
<li>Long division method</li>
9
<li>Long division method</li>
10
<li>Approximation method</li>
10
<li>Approximation method</li>
11
</ul><h2>Square Root of 4.2 by Long Division Method</h2>
11
</ul><h2>Square Root of 4.2 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>
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>
13
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4.2, we need to consider it as 4.2.</p>
13
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4.2, we need to consider it as 4.2.</p>
14
<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 4. We can say n is ‘2’ because 2 × 2 is equal to 4. Now the<a>quotient</a>is 2 after subtracting 4 from 4, the<a>remainder</a>is 0.</p>
14
<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 4. We can say n is ‘2’ because 2 × 2 is equal to 4. Now the<a>quotient</a>is 2 after subtracting 4 from 4, the<a>remainder</a>is 0.</p>
15
<p><strong>Step 3:</strong>Since we have a<a>decimal</a>, we bring down the next digit from the decimal part, which is 2, making the new<a>dividend</a>20.</p>
15
<p><strong>Step 3:</strong>Since we have a<a>decimal</a>, we bring down the next digit from the decimal part, which is 2, making the new<a>dividend</a>20.</p>
16
<p><strong>Step 4:</strong>Add the old<a>divisor</a>with the same number 2 + 2, we get 4, which will be our new divisor.</p>
16
<p><strong>Step 4:</strong>Add the old<a>divisor</a>with the same number 2 + 2, we get 4, which will be our new divisor.</p>
17
<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 20. Let's consider n as 0, now 4 × 0 × 0 = 0.</p>
17
<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 20. Let's consider n as 0, now 4 × 0 × 0 = 0.</p>
18
<p><strong>Step 6:</strong>Subtract 0 from 20, the difference is 20, and the quotient is 2.0.</p>
18
<p><strong>Step 6:</strong>Subtract 0 from 20, the difference is 20, and the quotient is 2.0.</p>
19
<p><strong>Step 7:</strong>Since the dividend is larger than the divisor, we bring down another set of zeroes to continue the division process.</p>
19
<p><strong>Step 7:</strong>Since the dividend is larger than the divisor, we bring down another set of zeroes to continue the division process.</p>
20
<p><strong>Step 8:</strong>Now we need to find the new divisor that fits the dividend. Repeat the steps to get more decimal places.</p>
20
<p><strong>Step 8:</strong>Now we need to find the new divisor that fits the dividend. Repeat the steps to get more decimal places.</p>
21
<p>So the square root of √4.2 ≈ 2.04939.</p>
21
<p>So the square root of √4.2 ≈ 2.04939.</p>
22
<h3>Explore Our Programs</h3>
22
<h3>Explore Our Programs</h3>
23
-
<p>No Courses Available</p>
24
<h2>Square Root of 4.2 by Approximation Method</h2>
23
<h2>Square Root of 4.2 by Approximation Method</h2>
25
<p>The approximation method is another method for finding the 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 4.2 using the approximation method.</p>
24
<p>The approximation method is another method for finding the 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 4.2 using the approximation method.</p>
26
<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √4.2. The smallest perfect square<a>less than</a>4.2 is 4, and the largest perfect square<a>greater than</a>4.2 is 9. √4.2 falls somewhere between 2 and 3.</p>
25
<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √4.2. The smallest perfect square<a>less than</a>4.2 is 4, and the largest perfect square<a>greater than</a>4.2 is 9. √4.2 falls somewhere between 2 and 3.</p>
27
<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Applying the formula: (4.2 - 4) / (9 - 4) = 0.2 / 5 = 0.04 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 2 + 0.04 ≈ 2.04, so the square root of 4.2 is approximately 2.04939.</p>
26
<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Applying the formula: (4.2 - 4) / (9 - 4) = 0.2 / 5 = 0.04 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 2 + 0.04 ≈ 2.04, so the square root of 4.2 is approximately 2.04939.</p>
28
<h2>Common Mistakes and How to Avoid Them in the Square Root of 4.2</h2>
27
<h2>Common Mistakes and How to Avoid Them in the Square Root of 4.2</h2>
29
<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
28
<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
30
<h3>Problem 1</h3>
29
<h3>Problem 1</h3>
31
<p>Can you help Max find the area of a square box if its side length is given as √4.2?</p>
30
<p>Can you help Max find the area of a square box if its side length is given as √4.2?</p>
32
<p>Okay, lets begin</p>
31
<p>Okay, lets begin</p>
33
<p>The area of the square is approximately 17.64 square units.</p>
32
<p>The area of the square is approximately 17.64 square units.</p>
34
<h3>Explanation</h3>
33
<h3>Explanation</h3>
35
<p>The area of the square = side².</p>
34
<p>The area of the square = side².</p>
36
<p>The side length is given as √4.2.</p>
35
<p>The side length is given as √4.2.</p>
37
<p>Area of the square = side² = √4.2 × √4.2 ≈ 2.04939 × 2.04939 ≈ 4.2</p>
36
<p>Area of the square = side² = √4.2 × √4.2 ≈ 2.04939 × 2.04939 ≈ 4.2</p>
38
<p>Therefore, the area of the square box is approximately 4.2 square units.</p>
37
<p>Therefore, the area of the square box is approximately 4.2 square units.</p>
39
<p>Well explained 👍</p>
38
<p>Well explained 👍</p>
40
<h3>Problem 2</h3>
39
<h3>Problem 2</h3>
41
<p>A square-shaped building measuring 4.2 square feet is built; if each of the sides is √4.2, what will be the square feet of half of the building?</p>
40
<p>A square-shaped building measuring 4.2 square feet is built; if each of the sides is √4.2, what will be the square feet of half of the building?</p>
42
<p>Okay, lets begin</p>
41
<p>Okay, lets begin</p>
43
<p>2.1 square feet</p>
42
<p>2.1 square feet</p>
44
<h3>Explanation</h3>
43
<h3>Explanation</h3>
45
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
44
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
46
<p>Dividing 4.2 by 2 = we get 2.1.</p>
45
<p>Dividing 4.2 by 2 = we get 2.1.</p>
47
<p>So half of the building measures 2.1 square feet.</p>
46
<p>So half of the building measures 2.1 square feet.</p>
48
<p>Well explained 👍</p>
47
<p>Well explained 👍</p>
49
<h3>Problem 3</h3>
48
<h3>Problem 3</h3>
50
<p>Calculate √4.2 × 5.</p>
49
<p>Calculate √4.2 × 5.</p>
51
<p>Okay, lets begin</p>
50
<p>Okay, lets begin</p>
52
<p>Approximately 10.24695</p>
51
<p>Approximately 10.24695</p>
53
<h3>Explanation</h3>
52
<h3>Explanation</h3>
54
<p>The first step is to find the square root of 4.2, which is approximately 2.04939, the second step is to multiply 2.04939 with 5.</p>
53
<p>The first step is to find the square root of 4.2, which is approximately 2.04939, the second step is to multiply 2.04939 with 5.</p>
55
<p>So 2.04939 × 5 ≈ 10.24695.</p>
54
<p>So 2.04939 × 5 ≈ 10.24695.</p>
56
<p>Well explained 👍</p>
55
<p>Well explained 👍</p>
57
<h3>Problem 4</h3>
56
<h3>Problem 4</h3>
58
<p>What will be the square root of (4.2 + 0.8)?</p>
57
<p>What will be the square root of (4.2 + 0.8)?</p>
59
<p>Okay, lets begin</p>
58
<p>Okay, lets begin</p>
60
<p>The square root is approximately 2.236</p>
59
<p>The square root is approximately 2.236</p>
61
<h3>Explanation</h3>
60
<h3>Explanation</h3>
62
<p>To find the square root, we need to find the sum of (4.2 + 0.8). 4.2 + 0.8 = 5, and then √5 ≈ 2.236.</p>
61
<p>To find the square root, we need to find the sum of (4.2 + 0.8). 4.2 + 0.8 = 5, and then √5 ≈ 2.236.</p>
63
<p>Therefore, the square root of (4.2 + 0.8) is approximately ±2.236.</p>
62
<p>Therefore, the square root of (4.2 + 0.8) is approximately ±2.236.</p>
64
<p>Well explained 👍</p>
63
<p>Well explained 👍</p>
65
<h3>Problem 5</h3>
64
<h3>Problem 5</h3>
66
<p>Find the perimeter of the rectangle if its length ‘l’ is √4.2 units and the width ‘w’ is 2 units.</p>
65
<p>Find the perimeter of the rectangle if its length ‘l’ is √4.2 units and the width ‘w’ is 2 units.</p>
67
<p>Okay, lets begin</p>
66
<p>Okay, lets begin</p>
68
<p>We find the perimeter of the rectangle as approximately 8.09878 units.</p>
67
<p>We find the perimeter of the rectangle as approximately 8.09878 units.</p>
69
<h3>Explanation</h3>
68
<h3>Explanation</h3>
70
<p>Perimeter of the rectangle = 2 × (length + width).</p>
69
<p>Perimeter of the rectangle = 2 × (length + width).</p>
71
<p>Perimeter = 2 × (√4.2 + 2) = 2 × (2.04939 + 2) ≈ 2 × 4.04939 ≈ 8.09878 units.</p>
70
<p>Perimeter = 2 × (√4.2 + 2) = 2 × (2.04939 + 2) ≈ 2 × 4.04939 ≈ 8.09878 units.</p>
72
<p>Well explained 👍</p>
71
<p>Well explained 👍</p>
73
<h2>FAQ on Square Root of 4.2</h2>
72
<h2>FAQ on Square Root of 4.2</h2>
74
<h3>1.What is √4.2 in its simplest form?</h3>
73
<h3>1.What is √4.2 in its simplest form?</h3>
75
<p>Since 4.2 is not a perfect square, √4.2 cannot be simplified further in<a>terms</a>of integers. The approximate value is 2.04939.</p>
74
<p>Since 4.2 is not a perfect square, √4.2 cannot be simplified further in<a>terms</a>of integers. The approximate value is 2.04939.</p>
76
<h3>2.Is 4.2 a perfect square?</h3>
75
<h3>2.Is 4.2 a perfect square?</h3>
77
<p>No, 4.2 is not a perfect square because it cannot be expressed as the<a>product</a>of an integer with itself.</p>
76
<p>No, 4.2 is not a perfect square because it cannot be expressed as the<a>product</a>of an integer with itself.</p>
78
<h3>3.Calculate the square of 4.2.</h3>
77
<h3>3.Calculate the square of 4.2.</h3>
79
<p>We get the square of 4.2 by multiplying the number by itself, that is 4.2 × 4.2 = 17.64.</p>
78
<p>We get the square of 4.2 by multiplying the number by itself, that is 4.2 × 4.2 = 17.64.</p>
80
<h3>4.Is 4.2 a rational number?</h3>
79
<h3>4.Is 4.2 a rational number?</h3>
81
<h3>5.Can √4.2 be expressed as a fraction?</h3>
80
<h3>5.Can √4.2 be expressed as a fraction?</h3>
82
<p>No, √4.2 is an irrational number and cannot be expressed exactly as a fraction.</p>
81
<p>No, √4.2 is an irrational number and cannot be expressed exactly as a fraction.</p>
83
<h2>Important Glossaries for the Square Root of 4.2</h2>
82
<h2>Important Glossaries for the Square Root of 4.2</h2>
84
<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>
83
<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>
85
</ul><ul><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>
84
</ul><ul><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>
86
</ul><ul><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>
85
</ul><ul><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>
87
</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.</li>
86
</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.</li>
88
</ul><ul><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: 4.2, 5.67, and 8.91 are decimals.</li>
87
</ul><ul><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: 4.2, 5.67, and 8.91 are decimals.</li>
89
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
88
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
90
<p>▶</p>
89
<p>▶</p>
91
<h2>Jaskaran Singh Saluja</h2>
90
<h2>Jaskaran Singh Saluja</h2>
92
<h3>About the Author</h3>
91
<h3>About the Author</h3>
93
<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>
92
<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>
94
<h3>Fun Fact</h3>
93
<h3>Fun Fact</h3>
95
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
94
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>