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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 4200</p>

4 <h2>What is the Square Root of 4200?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4200 is not a<a>perfect square</a>. The square root of 4200 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4200, whereas (4200)^(1/2) in the exponential form. √4200 ≈ 64.81, 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 4200</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>

8 <ul><li>Prime factorization method</li>

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 4200 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 4200 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 4200 Breaking it down, we get 2 × 2 × 3 × 5 × 5 × 7 × 2: 2^3 × 3^1 × 5^2 × 7^1</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 4200. The second step is to make pairs of those prime factors. Since 4200 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>

15 <p>Therefore, calculating 4200 using prime factorization is complicated without further simplification.</p>

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18 <h2>Square Root of 4200 by Long Division Method</h2>

17 <h2>Square Root of 4200 by Long Division Method</h2>

19 <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>

18 <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>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4200, we need to group it as 00 and 42.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4200, we need to group it as 00 and 42.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 42. We can say n as ‘6’ because 6 × 6 = 36 is less than 42. Now the<a>quotient</a>is 6 after subtracting 36 from 42, the<a>remainder</a>is 6.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 42. We can say n as ‘6’ because 6 × 6 = 36 is less than 42. Now the<a>quotient</a>is 6 after subtracting 36 from 42, the<a>remainder</a>is 6.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 00 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 6 + 6 = 12, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 00 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 6 + 6 = 12, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The next step is finding 12n × n ≤ 600. We can consider n as 4, now 12 × 4 = 48, and 484 × 4 = 1936.</p>

22 <p><strong>Step 4:</strong>The next step is finding 12n × n ≤ 600. We can consider n as 4, now 12 × 4 = 48, and 484 × 4 = 1936.</p>

24 <p><strong>Step 5:</strong>Subtract 1936 from 6000, the difference is 4064, and the quotient is 64.</p>

23 <p><strong>Step 5:</strong>Subtract 1936 from 6000, the difference is 4064, and the quotient is 64.</p>

25 <p><strong>Step 6:</strong>Since the dividend is greater than the divisor, we continue the process of adding decimals and bringing down zeroes. Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 406400.</p>

24 <p><strong>Step 6:</strong>Since the dividend is greater than the divisor, we continue the process of adding decimals and bringing down zeroes. Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 406400.</p>

26 <p><strong>Step 7:</strong>We continue the process to find the new divisor and quotient until we reach an approximation.</p>

25 <p><strong>Step 7:</strong>We continue the process to find the new divisor and quotient until we reach an approximation.</p>

27 <p>So the square root of √4200 ≈ 64.81</p>

26 <p>So the square root of √4200 ≈ 64.81</p>

28 <h2>Square Root of 4200 by Approximation Method</h2>

27 <h2>Square Root of 4200 by Approximation Method</h2>

29 <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 4200 using the approximation method.</p>

28 <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 4200 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √4200. The smallest perfect square less than 4200 is 4096 (64^2) and the largest perfect square<a>greater than</a>4200 is 4225 (65^2). √4200 falls somewhere between 64 and 65.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √4200. The smallest perfect square less than 4200 is 4096 (64^2) and the largest perfect square<a>greater than</a>4200 is 4225 (65^2). √4200 falls somewhere between 64 and 65.</p>

31 <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: (4200 - 4096) / (4225 - 4096) = 104 / 129 = 0.8062 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number which is 64 + 0.81 ≈ 64.81, so the square root of 4200 is approximately 64.81.</p>

30 <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: (4200 - 4096) / (4225 - 4096) = 104 / 129 = 0.8062 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number which is 64 + 0.81 ≈ 64.81, so the square root of 4200 is approximately 64.81.</p>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4200</h2>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4200</h2>

33 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

32 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

33 + <h2>Download Worksheets</h2>

34 <h3>Problem 1</h3>

35 <p>Can you help Max find the area of a square box if its side length is given as √4200?</p>

36 <p>Okay, lets begin</p>

37 <p>The area of the square is 4200 square units.</p>

38 <h3>Explanation</h3>

39 <p>The area of the square = side^2.</p>

40 <p>The side length is given as √4200.</p>

41 <p>Area of the square = side^2 = √4200 × √4200 = 4200.</p>

42 <p>Therefore, the area of the square box is 4200 square units.</p>

43 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

45 <p>A square-shaped building measuring 4200 square feet is built; if each of the sides is √4200, what will be the square feet of half of the building?</p>

46 <p>Okay, lets begin</p>

47 <p>2100 square feet.</p>

48 <h3>Explanation</h3>

49 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

50 <p>Dividing 4200 by 2 = we get 2100.</p>

51 <p>So half of the building measures 2100 square feet.</p>

52 <p>Well explained 👍</p>

53 <h3>Problem 3</h3>

54 <p>Calculate √4200 × 5.</p>

55 <p>Okay, lets begin</p>

56 <p>Approximately 324.05.</p>

57 <h3>Explanation</h3>

58 <p>The first step is to find the square root of 4200 which is approximately 64.81, the second step is to multiply 64.81 with 5.</p>

59 <p>So 64.81 × 5 ≈ 324.05.</p>

60 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

62 <p>What will be the square root of (4200 + 25)?</p>

63 <p>Okay, lets begin</p>

64 <p>The square root is approximately 65.</p>

65 <h3>Explanation</h3>

66 <p>To find the square root, we need to find the sum of (4200 + 25).</p>

67 <p>4200 + 25 = 4225, and then √4225 = 65.</p>

68 <p>Therefore, the square root of (4200 + 25) is ±65.</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of the rectangle if its length ‘l’ is √4200 units and the width ‘w’ is 38 units.</p>

72 <p>Okay, lets begin</p>

73 <p>Approximately 205.61 units.</p>

74 <h3>Explanation</h3>

75 <p>Perimeter of the rectangle = 2 × (length + width).</p>

76 <p>Perimeter = 2 × (√4200 + 38)</p>

77 <p>= 2 × (64.81 + 38)</p>

78 <p>= 2 × 102.81</p>

79 <p>≈ 205.61 units.</p>

80 <p>Well explained 👍</p>

81 <h2>FAQ on Square Root of 4200</h2>

82 <h3>1.What is √4200 in its simplest form?</h3>

83 <p>The prime factorization of 4200 is 2 × 2 × 2 × 3 × 5 × 5 × 7, so the simplest form of √4200 = √(2^3 × 3 × 5^2 × 7).</p>

84 <h3>2.Mention the factors of 4200.</h3>

85 <p>Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 1400, 2100, and 4200.</p>

86 <h3>3.Calculate the square of 4200.</h3>

87 <p>We get the square of 4200 by multiplying the number by itself, that is 4200 × 4200 = 17,640,000.</p>

88 <h3>4.Is 4200 a prime number?</h3>

89 <p>4200 is not a<a>prime number</a>, as it has more than two factors.</p>

90 <h3>5.4200 is divisible by?</h3>

91 <p>4200 has many factors; some of them are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 1400, 2100, and 4200.</p>

92 <h2>Important Glossaries for the Square Root of 4200</h2>

93 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root that is √16 = 4. </li>

94 <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>

95 <li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that is more commonly used in practical applications. </li>

96 <li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 36 is a perfect square because it is 6^2. </li>

97 <li><strong>Prime factorization:</strong>The breaking down of a number into its basic prime factors. For example, the prime factorization of 4200 is 2^3 × 3^1 × 5^2 × 7^1.</li>

98 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

99 <p>▶</p>

100 <h2>Jaskaran Singh Saluja</h2>

101 <h3>About the Author</h3>

102 <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>

103 <h3>Fun Fact</h3>

104 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>