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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 4425.</p>

4 <h2>What is the Square Root of 4425?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4425 is not a<a>perfect square</a>. The square root of 4425 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4425, whereas (4425)^(1/2) in the exponential form. √4425 ≈ 66.4906, 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 4425</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 4425 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 4425 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 4425</p>

14 <p>Breaking it down, we get 3 x 3 x 5 x 5 x 59.</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 4425. The second step is to make pairs of those prime factors. Since 4425 is not a perfect square, therefore the digits of the number can’t be grouped in pairs entirely. Therefore, calculating 4425 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 4425 by Long Division Method</h2>

17 <h2>Square Root of 4425 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 4425, we need to group it as 42 and 25.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4425, we need to group it as 42 and 25.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 42. We can say n as '6' because 6 x 6 = 36, which is lesser than 42. Now the<a>quotient</a>is 6 after subtracting 42 - 36, the<a>remainder</a>is 6.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 42. We can say n as '6' because 6 x 6 = 36, which is lesser than 42. Now the<a>quotient</a>is 6 after subtracting 42 - 36, the<a>remainder</a>is 6.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 25, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 6 + 6, we get 12, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 25, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 6 + 6, we get 12, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>We find n such that 12n x n ≤ 625. Let us consider n as 5, now 12 x 5 x 5 = 625.</p>

22 <p><strong>Step 4:</strong>We find n such that 12n x n ≤ 625. Let us consider n as 5, now 12 x 5 x 5 = 625.</p>

24 <p><strong>Step 5:</strong>Subtract 625 from 625, the difference is 0, and the quotient is 65.</p>

23 <p><strong>Step 5:</strong>Subtract 625 from 625, the difference is 0, and the quotient is 65.</p>

25 <p><strong>Step 6:</strong>Since the remainder is zero, the square root of 4425 is approximately 66.49, but the process of attaining further<a>decimal</a>places can continue.</p>

24 <p><strong>Step 6:</strong>Since the remainder is zero, the square root of 4425 is approximately 66.49, but the process of attaining further<a>decimal</a>places can continue.</p>

26 <h2>Square Root of 4425 by Approximation Method</h2>

25 <h2>Square Root of 4425 by Approximation Method</h2>

27 <p>The approximation method is another method for finding the 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 4425 using the approximation method.</p>

26 <p>The approximation method is another method for finding the 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 4425 using the approximation method.</p>

28 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √4425. The smallest perfect square<a>less than</a>4425 is 4356 (66^2) and the largest perfect square<a>greater than</a>4425 is 4489 (67^2). √4425 falls somewhere between 66 and 67.</p>

27 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √4425. The smallest perfect square<a>less than</a>4425 is 4356 (66^2) and the largest perfect square<a>greater than</a>4425 is 4489 (67^2). √4425 falls somewhere between 66 and 67.</p>

29 <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) Going by the formula (4425 - 4356) / (4489 - 4356) = 69/133 ≈ 0.518 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 66 + 0.518 ≈ 66.518, so the square root of 4425 is approximately 66.52.</p>

28 <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) Going by the formula (4425 - 4356) / (4489 - 4356) = 69/133 ≈ 0.518 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 66 + 0.518 ≈ 66.518, so the square root of 4425 is approximately 66.52.</p>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4425</h2>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4425</h2>

31 <p>Students do make mistakes while finding the square root, likewise 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>

30 <p>Students do make mistakes while finding the square root, likewise 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>

31 + <h2>Download Worksheets</h2>

32 <h3>Problem 1</h3>

33 <p>Can you help Max find the area of a square box if its side length is given as √4425?</p>

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

35 <p>The area of the square is approximately 4425 square units.</p>

36 <h3>Explanation</h3>

37 <p>The area of the square = side².</p>

38 <p>The side length is given as √4425.</p>

39 <p>Area of the square = side² = (√4425) x (√4425) = 4425.</p>

40 <p>Therefore, the area of the square box is approximately 4425 square units.</p>

41 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

43 <p>A square-shaped building measuring 4425 square feet is built; if each of the sides is √4425, what will be the square feet of half of the building?</p>

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

45 <p>2212.5 square feet</p>

46 <h3>Explanation</h3>

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

48 <p>Dividing 4425 by 2 = we get 2212.5.</p>

49 <p>So half of the building measures 2212.5 square feet.</p>

50 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

52 <p>Calculate √4425 x 3.</p>

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

54 <p>199.4718</p>

55 <h3>Explanation</h3>

56 <p>The first step is to find the square root of 4425 which is approximately 66.49, the second step is to multiply 66.49 with 3.</p>

57 <p>So 66.49 x 3 ≈ 199.4718.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

60 <p>What will be the square root of (4250 + 175)?</p>

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

62 <p>The square root is approximately 67.</p>

63 <h3>Explanation</h3>

64 <p>To find the square root, we need to find the sum of (4250 + 175). 4250 + 175 = 4425, and then √4425 ≈ 66.49.</p>

65 <p>Therefore, the square root of (4250 + 175) is approximately ±67.</p>

66 <p>Well explained 👍</p>

67 <h3>Problem 5</h3>

68 <p>Find the perimeter of the rectangle if its length ‘l’ is √4425 units and the width ‘w’ is 50 units.</p>

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

70 <p>We find the perimeter of the rectangle as approximately 232.98 units.</p>

71 <h3>Explanation</h3>

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

73 <p>Perimeter = 2 × (√4425 + 50) = 2 × (66.49 + 50) = 2 × 116.49 = 232.98 units.</p>

74 <p>Well explained 👍</p>

75 <h2>FAQ on Square Root of 4425</h2>

76 <h3>1.What is √4425 in its simplest form?</h3>

77 <p>The prime factorization of 4425 is 3 x 3 x 5 x 5 x 59, so the simplest form of √4425 = √(3 x 3 x 5 x 5 x 59).</p>

78 <h3>2.Mention the factors of 4425.</h3>

79 <p>Factors of 4425 include 1, 3, 5, 9, 15, 25, 45, 59, 75, 177, 295, 885, and 4425.</p>

80 <h3>3.Calculate the square of 4425.</h3>

81 <p>We get the square of 4425 by multiplying the number by itself, that is, 4425 x 4425 = 19,602,625.</p>

82 <h3>4.Is 4425 a prime number?</h3>

83 <p>4425 is not a<a>prime number</a>, as it has more than two factors.</p>

84 <h3>5.4425 is divisible by?</h3>

85 <p>4425 has<a>multiple</a>factors including 1, 3, 5, 9, 15, 25, 45, 59, 75, 177, 295, 885, and 4425.</p>

86 <h2>Important Glossaries for the Square Root of 4425</h2>

87 <ul><li><strong>Square root:</strong>A square root is a value that, when multiplied by itself, gives the original number. Example: 4^2 = 16 and the inverse of the square is the square root that is √16 = 4.</li>

88 </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>

89 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, however, it is always a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.</li>

90 </ul><ul><li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as a product of its prime factors. Example: The prime factorization of 28 is 2 x 2 x 7.</li>

91 </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: 7.86, 8.65, and 9.42 are decimals.</li>

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

93 <p>▶</p>

94 <h2>Jaskaran Singh Saluja</h2>

95 <h3>About the Author</h3>

96 <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>

97 <h3>Fun Fact</h3>

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