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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 2404.</p>

4 <h2>What is the Square Root of 2404?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 2404 is not a<a>perfect square</a>. The square root of 2404 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2404, whereas in<a>exponential form</a>it is (2404)^(1/2). √2404 ≈ 49.034, 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 2404</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>and approximation methods 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 2404 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 2404 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 2404 Breaking it down, we get 2 × 2 × 601: 2² × 601</p>

14 <p><strong>Step 2:</strong>Since 2404 is not a perfect square, we can't group the digits into pairs.</p>

15 <p>Therefore, calculating 2404 using prime factorization is impossible.</p>

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18 <h2>Square Root of 2404 by Long Division Method</h2>

17 <h2>Square Root of 2404 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 2404, we group it as 24 and 04.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 2404, we group it as 24 and 04.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 24. We can say n is 4 because 4 × 4 = 16, which is less than 24. The<a>quotient</a>is 4, and the<a>remainder</a>is 24 - 16 = 8.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 24. We can say n is 4 because 4 × 4 = 16, which is less than 24. The<a>quotient</a>is 4, and the<a>remainder</a>is 24 - 16 = 8.</p>

22 <p><strong>Step 3:</strong>Bring down 04 to make the new<a>dividend</a>804. Add the old<a>divisor</a>(4) with the same number, 4 + 4 = 8, which will be our new divisor's tens digit.</p>

21 <p><strong>Step 3:</strong>Bring down 04 to make the new<a>dividend</a>804. Add the old<a>divisor</a>(4) with the same number, 4 + 4 = 8, which will be our new divisor's tens digit.</p>

23 <p><strong>Step 4:</strong>We need to find a number n such that (80 + n) × n ≤ 804. Let n be 9, because 89 × 9 = 801.</p>

22 <p><strong>Step 4:</strong>We need to find a number n such that (80 + n) × n ≤ 804. Let n be 9, because 89 × 9 = 801.</p>

24 <p><strong>Step 5:</strong>Subtract 801 from 804. The new remainder is 3.</p>

23 <p><strong>Step 5:</strong>Subtract 801 from 804. The new remainder is 3.</p>

25 <p><strong>Step 6:</strong>Since the remainder is less than the divisor, add a decimal point and two zeroes to the dividend. Now the new dividend is 300.</p>

24 <p><strong>Step 6:</strong>Since the remainder is less than the divisor, add a decimal point and two zeroes to the dividend. Now the new dividend is 300.</p>

26 <p><strong>Step 7:</strong>The next divisor will be (89 × 10) + n, we need n such that (890 + n) × n ≤ 300, leading us to n as 0. Repeat these steps until the desired precision is achieved.</p>

25 <p><strong>Step 7:</strong>The next divisor will be (89 × 10) + n, we need n such that (890 + n) × n ≤ 300, leading us to n as 0. Repeat these steps until the desired precision is achieved.</p>

27 <p>The quotient will approximate to √2404 = 49.034.</p>

26 <p>The quotient will approximate to √2404 = 49.034.</p>

28 <h2>Square Root of 2404 by Approximation Method</h2>

27 <h2>Square Root of 2404 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 2404 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 2404 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Find the closest perfect squares around √2404. The smallest perfect square near 2404 is 2401, and the largest is 2500. √2404 falls between √2401 = 49 and √2500 = 50.</p>

29 <p><strong>Step 1:</strong>Find the closest perfect squares around √2404. The smallest perfect square near 2404 is 2401, and the largest is 2500. √2404 falls between √2401 = 49 and √2500 = 50.</p>

31 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (2404 - 2401) / (2500 - 2401) = 3 / 99 ≈ 0.03</p>

30 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (2404 - 2401) / (2500 - 2401) = 3 / 99 ≈ 0.03</p>

32 <p>Add this to 49 to get the approximate square root: 49 + 0.03 = 49.03.</p>

31 <p>Add this to 49 to get the approximate square root: 49 + 0.03 = 49.03.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 2404</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 2404</h2>

34 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let's look at a few common mistakes in detail.</p>

33 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let's look at a few common mistakes in detail.</p>

34 + <h2>Download Worksheets</h2>

35 <h3>Problem 1</h3>

36 <p>Can you help Max find the area of a square box if its side length is given as √2404?</p>

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

38 <p>The area of the square is approximately 5777.632 square units.</p>

39 <h3>Explanation</h3>

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

41 <p>The side length is given as √2404.</p>

42 <p>Area of the square = side² = √2404 × √2404 ≈ 49.034 × 49.034 ≈ 5777.632</p>

43 <p>Therefore, the area of the square box is approximately 5777.632 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped garden measures 2404 square feet. If each side is √2404, what will be the square feet of half of the garden?</p>

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

48 <p>1202 square feet</p>

49 <h3>Explanation</h3>

50 <p>We can just divide the given area by 2 since the garden is square-shaped.</p>

51 <p>Dividing 2404 by 2, we get 1202.</p>

52 <p>So half of the garden measures 1202 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √2404 × 5.</p>

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

57 <p>Approximately 245.17</p>

58 <h3>Explanation</h3>

59 <p>First, find the square root of 2404, which is approximately 49.034.</p>

60 <p>Then multiply 49.034 by 5. 49.034 × 5 ≈ 245.17</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 4</h3>

63 <p>What will be the square root of (2400 + 4)?</p>

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

65 <p>The square root is approximately 49.034</p>

66 <h3>Explanation</h3>

67 <p>To find the square root, we need to find the sum of (2400 + 4) 2400 + 4 = 2404, and then √2404 ≈ 49.034</p>

68 <p>Therefore, the square root of (2400 + 4) is approximately ±49.034</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of a rectangle if its length ‘l’ is √2404 units and the width ‘w’ is 40 units.</p>

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

73 <p>Approximately 178.068 units</p>

74 <h3>Explanation</h3>

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

76 <p>Perimeter = 2 × (√2404 + 40) ≈ 2 × (49.034 + 40) ≈ 2 × 89.034 ≈ 178.068 units.</p>

77 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 2404</h2>

79 <h3>1.What is √2404 in its simplest form?</h3>

80 <p>The prime factorization of 2404 is 2 × 2 × 601, so the simplest form of √2404 = √(2 × 2 × 601).</p>

81 <h3>2.Mention the factors of 2404.</h3>

82 <p>Factors of 2404 are 1, 2, 4, 601, 1202, and 2404.</p>

83 <h3>3.Calculate the square of 2404.</h3>

84 <p>We get the square of 2404 by multiplying the number by itself, which is 2404 × 2404 = 5777616.</p>

85 <h3>4.Is 2404 a prime number?</h3>

86 <p>2404 is not a<a>prime number</a>, as it has more than two factors.</p>

87 <h3>5.2404 is divisible by?</h3>

88 <p>2404 is divisible by the factors 1, 2, 4, 601, 1202, and 2404.</p>

89 <h2>Important Glossaries for the Square Root of 2404</h2>

90 <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>

91 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

92 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the positive square root is more commonly used and is known as the principal square root.</li>

93 </ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors.</li>

94 </ul><ul><li><strong>Long division method:</strong>A step-by-step approach used to find the square root of non-perfect squares.</li>

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

96 <p>▶</p>

97 <h2>Jaskaran Singh Saluja</h2>

98 <h3>About the Author</h3>

99 <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>

100 <h3>Fun Fact</h3>

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