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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 fields such as vehicle design, finance, and more. Here, we will discuss the square root of 1824.</p>

4 <h2>What is the Square Root of 1824?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1824 is not a<a>perfect square</a>. The square root of 1824 is expressed in both radical and exponential forms. In radical form, it is expressed as √1824, whereas in<a>exponential form</a>it is expressed as (1824)^(1/2). √1824 ≈ 42.708, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>of two<a>integers</a>.</p>

6 <h2>Finding the Square Root of 1824</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<a>long 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 1824 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 1824 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1824 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 3 x 19 =<a>2^5</a>x 3 x 19</p>

14 <p><strong>Step 2:</strong>Now we found the prime factors of 1824. The second step is to make pairs of those prime factors. Since 1824 is not a perfect square, the digits of the number can’t be grouped in pairs evenly.</p>

15 <p>Therefore, calculating 1824 using prime factorization directly is complex, and other methods are preferred.</p>

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18 <h2>Square Root of 1824 by Long Division Method</h2>

17 <h2>Square Root of 1824 by Long Division Method</h2>

19 <p>The long<a>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 long<a>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, group the digits in pairs from right to left. In the case of 1824, group them as 18 and 24.</p>

19 <p><strong>Step 1:</strong>To begin with, group the digits in pairs from right to left. In the case of 1824, group them as 18 and 24.</p>

21 <p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 18. We can say n is 4 because 4^2 = 16, which is less than 18. Now the<a>quotient</a>is 4, and the<a>remainder</a>is 2.</p>

20 <p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 18. We can say n is 4 because 4^2 = 16, which is less than 18. Now the<a>quotient</a>is 4, and the<a>remainder</a>is 2.</p>

22 <p><strong>Step 3:</strong>Bring down the next pair 24, making the new<a>dividend</a>224. Add the old<a>divisor</a>with the same number: 4 + 4 = 8, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair 24, making the new<a>dividend</a>224. Add the old<a>divisor</a>with the same number: 4 + 4 = 8, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor will be 8n. We need to find the value of n such that 8n x n ≤ 224.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 8n. We need to find the value of n such that 8n x n ≤ 224.</p>

24 <p><strong>Step 5:</strong>Consider n as 2. Then 82 x 2 = 164.</p>

23 <p><strong>Step 5:</strong>Consider n as 2. Then 82 x 2 = 164.</p>

25 <p><strong>Step 6:</strong>Subtract 164 from 224, the difference is 60, and the quotient is 42.</p>

24 <p><strong>Step 6:</strong>Subtract 164 from 224, the difference is 60, and the quotient is 42.</p>

26 <p><strong>Step 7:</strong>Since the dividend is less than the divisor, add a decimal point and bring down two zeros, making the dividend 6000.</p>

25 <p><strong>Step 7:</strong>Since the dividend is less than the divisor, add a decimal point and bring down two zeros, making the dividend 6000.</p>

27 <p><strong>Step 8:</strong>Find n such that 842 x n ≤ 6000. Let n be 7. Then 842 x 7 = 5894.</p>

26 <p><strong>Step 8:</strong>Find n such that 842 x n ≤ 6000. Let n be 7. Then 842 x 7 = 5894.</p>

28 <p><strong>Step 9:</strong>Subtract 5894 from 6000, resulting in 106.</p>

27 <p><strong>Step 9:</strong>Subtract 5894 from 6000, resulting in 106.</p>

29 <p><strong>Step 10:</strong>The quotient is 42.7.</p>

28 <p><strong>Step 10:</strong>The quotient is 42.7.</p>

30 <p><strong>Step 11:</strong>Continue these steps until you get two decimal places.</p>

29 <p><strong>Step 11:</strong>Continue these steps until you get two decimal places.</p>

31 <p>So the square root of √1824 is approximately 42.708.</p>

30 <p>So the square root of √1824 is approximately 42.708.</p>

32 <h2>Square Root of 1824 by Approximation Method</h2>

31 <h2>Square Root of 1824 by Approximation Method</h2>

33 <p>Approximation 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 1824 using the approximation method.</p>

32 <p>Approximation 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 1824 using the approximation method.</p>

34 <p><strong>Step 1:</strong>Find the closest perfect squares around √1824. The smallest perfect square less than 1824 is 1764 (42^2), and the largest perfect square<a>greater than</a>1824 is 1849 (43^2). √1824 falls between 42 and 43.</p>

33 <p><strong>Step 1:</strong>Find the closest perfect squares around √1824. The smallest perfect square less than 1824 is 1764 (42^2), and the largest perfect square<a>greater than</a>1824 is 1849 (43^2). √1824 falls between 42 and 43.</p>

35 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (1824 - 1764) / (1849 - 1764) = 60/85 ≈ 0.70588</p>

34 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (1824 - 1764) / (1849 - 1764) = 60/85 ≈ 0.70588</p>

36 <p>Using the formula, add the result to the lower perfect square root: 42 + 0.70588 ≈ 42.71, so the square root of 1824 is approximately 42.71.</p>

35 <p>Using the formula, add the result to the lower perfect square root: 42 + 0.70588 ≈ 42.71, so the square root of 1824 is approximately 42.71.</p>

37 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1824</h2>

36 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1824</h2>

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

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

38 + <h2>Download Worksheets</h2>

39 <h3>Problem 1</h3>

40 <p>Can you help Max find the area of a square box if its side length is given as √1824?</p>

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

42 <p>The area of the square is approximately 3324.096 square units.</p>

43 <h3>Explanation</h3>

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

45 <p>The side length is given as √1824.</p>

46 <p>Area of the square = side^2 = √1824 x √1824 ≈ 42.708 x 42.708 ≈ 1824.</p>

47 <p>Therefore, the area of the square box is approximately 3324.096 square units.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 2</h3>

50 <p>A square-shaped garden measuring 1824 square feet is built; if each of the sides is √1824, what will be the square feet of half of the garden?</p>

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

52 <p>912 square feet</p>

53 <h3>Explanation</h3>

54 <p>Since the garden is square-shaped, we can divide the total area by 2 to find half of it.</p>

55 <p>Dividing 1824 by 2 gives 912. So half of the garden measures 912 square feet.</p>

56 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

58 <p>Calculate √1824 x 5.</p>

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

60 <p>Approximately 213.54</p>

61 <h3>Explanation</h3>

62 <p>First, find the square root of 1824, which is approximately 42.708.</p>

63 <p>Then multiply 42.708 by 5. So, 42.708 x 5 ≈ 213.54.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

66 <p>What will be the square root of (1624 + 200)?</p>

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

68 <p>The square root is approximately 43.</p>

69 <h3>Explanation</h3>

70 <p>To find the square root, first find the sum of (1624 + 200).</p>

71 <p>1624 + 200 = 1824.</p>

72 <p>The square root of 1824 is approximately 42.708.</p>

73 <p>Therefore, the square root of (1624 + 200) is approximately 42.708.</p>

74 <p>Well explained 👍</p>

75 <h3>Problem 5</h3>

76 <p>Find the perimeter of a rectangle if its length ‘l’ is √1824 units and the width ‘w’ is 38 units.</p>

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

78 <p>The perimeter of the rectangle is approximately 161.42 units.</p>

79 <h3>Explanation</h3>

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

81 <p>Perimeter = 2 × (√1824 + 38) ≈ 2 × (42.708 + 38) ≈ 2 × 80.708 ≈ 161.42 units.</p>

82 <p>Well explained 👍</p>

83 <h2>FAQ on Square Root of 1824</h2>

84 <h3>1.What is √1824 in its simplest form?</h3>

85 <p>The prime factorization of 1824 is 2^5 x 3 x 19, so the simplest form of √1824 cannot be further simplified exactly, as it is an irrational number.</p>

86 <h3>2.Mention the factors of 1824.</h3>

87 <p>Factors of 1824 include 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 608, 912, and 1824.</p>

88 <h3>3.Calculate the square of 1824.</h3>

89 <p>We get the square of 1824 by multiplying the number by itself: 1824 x 1824 = 3,328,576.</p>

90 <h3>4.Is 1824 a prime number?</h3>

91 <p>1824 is not a<a>prime number</a>, as it has more than two factors.</p>

92 <h3>5.1824 is divisible by?</h3>

93 <p>1824 has many factors; it is divisible by 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 608, 912, and 1824.</p>

94 <h2>Important Glossaries for the Square Root of 1824</h2>

95 <ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, if 5^2 = 25, then the square root of 25 is √25 = 5.</li>

96 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be written as a simple fraction; its decimal form is non-repeating and non-terminating. For example, √2 is irrational.</li>

97 </ul><ul><li><strong>Prime factorization:</strong>Expressing a number as the product of its prime factors. For example, the prime factorization of 1824 is 2^5 x 3 x 19.</li>

98 </ul><ul><li><strong>Long division method:</strong>A method used to find the square root of a number that is not a perfect square by dividing the number into pairs of digits and using a series of steps.</li>

99 </ul><ul><li><strong>Approximation method:</strong>A method used to estimate the square root of a number by identifying nearby perfect squares and using interpolation to find a more precise value.</li>

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

101 <p>▶</p>

102 <h2>Jaskaran Singh Saluja</h2>

103 <h3>About the Author</h3>

104 <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>

105 <h3>Fun Fact</h3>

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