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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 and finance. Here, we will discuss the square root of 4840.</p>

4 <h2>What is the Square Root of 4840?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4840 is not a<a>perfect square</a>. The square root of 4840 is expressed in both radical and exponential forms. In the radical form, it is expressed as √4840, whereas in the<a>exponential form</a>it is expressed as (4840)^(1/2). √4840 ≈ 69.535, 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 4840</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 4840 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 4840 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 4840</p>

14 <p>Breaking it down, we get 2 × 2 × 2 × 5 × 11 × 11: 2^3 × 5^1 × 11^2</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 4840. The second step is to make pairs of those prime factors. Since 4840 is not a perfect square, the digits of the number can’t be grouped in pairs perfectly. Therefore, calculating √4840 using prime factorization will only give an approximate value.</p>

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18 <h2>Square Root of 4840 by Long Division Method</h2>

17 <h2>Square Root of 4840 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, we need to group the numbers from right to left. In the case of 4840, we need to group it as 48 and 40.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4840, we need to group it as 48 and 40.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 48. We can say n is ‘6’ because 6 × 6 = 36, which is less than or equal to 48. Now the<a>quotient</a>is 6. Subtracting 36 from 48, the<a>remainder</a>is 12.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 48. We can say n is ‘6’ because 6 × 6 = 36, which is less than or equal to 48. Now the<a>quotient</a>is 6. Subtracting 36 from 48, the<a>remainder</a>is 12.</p>

22 <p><strong>Step 3:</strong>Bring down 40, 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>Bring down 40, 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 new divisor will be 12n. We need to find the value of n such that 12n × n is less than or equal to 1240. Let us consider n as 9: 129 × 9 = 1161.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 12n. We need to find the value of n such that 12n × n is less than or equal to 1240. Let us consider n as 9: 129 × 9 = 1161.</p>

24 <p><strong>Step 5:</strong>Subtracting 1161 from 1240 gives a remainder of 79.</p>

23 <p><strong>Step 5:</strong>Subtracting 1161 from 1240 gives a remainder of 79.</p>

25 <p><strong>Step 6:</strong>Since the dividend is less than the new divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7900.</p>

24 <p><strong>Step 6:</strong>Since the dividend is less than the new divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7900.</p>

26 <p><strong>Step 7:</strong>Find the new divisor, which is 138. Continuing this process will yield the square root of 4840 as approximately 69.535.</p>

25 <p><strong>Step 7:</strong>Find the new divisor, which is 138. Continuing this process will yield the square root of 4840 as approximately 69.535.</p>

27 <h2>Square Root of 4840 by Approximation Method</h2>

26 <h2>Square Root of 4840 by Approximation Method</h2>

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 4840 using the approximation method.</p>

27 <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 4840 using the approximation method.</p>

29 <p><strong>Step 1:</strong>We need to find the closest perfect squares to 4840. The smallest perfect square less than 4840 is 4761 (69^2), and the largest perfect square<a>greater than</a>4840 is 4900 (70^2). √4840 falls somewhere between 69 and 70.</p>

28 <p><strong>Step 1:</strong>We need to find the closest perfect squares to 4840. The smallest perfect square less than 4840 is 4761 (69^2), and the largest perfect square<a>greater than</a>4840 is 4900 (70^2). √4840 falls somewhere between 69 and 70.</p>

30 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (4840 - 4761) / (4900 - 4761) ≈ 0.535 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the initial integer value to the decimal number: 69 + 0.535 = 69.535, so the square root of 4840 is approximately 69.535.</p>

29 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (4840 - 4761) / (4900 - 4761) ≈ 0.535 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the initial integer value to the decimal number: 69 + 0.535 = 69.535, so the square root of 4840 is approximately 69.535.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4840</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4840</h2>

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

31 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few mistakes that students tend to make in detail.</p>

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33 <h3>Problem 1</h3>

34 <p>Can you help Max find the area of a square box if its side length is given as √4840?</p>

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

36 <p>The area of the square is approximately 4840 square units.</p>

37 <h3>Explanation</h3>

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

39 <p>The side length is given as √4840.</p>

40 <p>Area of the square = side^2 = √4840 × √4840 = 4840.</p>

41 <p>Therefore, the area of the square box is approximately 4840 square units.</p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 4840 square feet is built; if each of the sides is √4840, what will be the square feet of half of the building?</p>

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

46 <p>2420 square feet</p>

47 <h3>Explanation</h3>

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

49 <p>Dividing 4840 by 2 = we get 2420.</p>

50 <p>So half of the building measures 2420 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √4840 × 5.</p>

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

55 <p>Approximately 347.675</p>

56 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 4840, which is approximately 69.535.</p>

58 <p>The second step is to multiply 69.535 by 5.</p>

59 <p>So 69.535 × 5 ≈ 347.675.</p>

60 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

62 <p>What will be the square root of (4840 + 60)?</p>

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

64 <p>The square root is approximately 70.5.</p>

65 <h3>Explanation</h3>

66 <p>To find the square root, we need to find the sum of (4840 + 60). 4840 + 60 = 4900, and then √4900 = 70.</p>

67 <p>Therefore, the square root of (4840 + 60) is ±70.</p>

68 <p>Well explained 👍</p>

69 <h3>Problem 5</h3>

70 <p>Find the perimeter of the rectangle if its length ‘l’ is √4840 units and the width ‘w’ is 60 units.</p>

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

72 <p>The perimeter of the rectangle is approximately 259.07 units.</p>

73 <h3>Explanation</h3>

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

75 <p>Perimeter = 2 × (√4840 + 60) = 2 × (69.535 + 60) ≈ 2 × 129.535 ≈ 259.07 units.</p>

76 <p>Well explained 👍</p>

77 <h2>FAQ on Square Root of 4840</h2>

78 <h3>1.What is √4840 in its simplest form?</h3>

79 <p>The prime factorization of 4840 is 2 × 2 × 2 × 5 × 11 × 11, so the simplest form of √4840 is √(2^3 × 5 × 11^2).</p>

80 <h3>2.Mention the factors of 4840.</h3>

81 <p>Factors of 4840 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 242, 440, 484, 1210, 2420, and 4840.</p>

82 <h3>3.Calculate the square of 4840.</h3>

83 <p>We get the square of 4840 by multiplying the number by itself, that is 4840 × 4840 = 23,425,600.</p>

84 <h3>4.Is 4840 a prime number?</h3>

85 <p>4840 is not a<a>prime number</a>, as it has more than two factors.</p>

86 <h3>5.4840 is divisible by?</h3>

87 <p>4840 has many factors; those are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 242, 440, 484, 1210, 2420, and 4840.</p>

88 <h2>Important Glossaries for the Square Root of 4840</h2>

89 <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>

90 </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>

91 </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 a principal square root.</li>

92 </ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of a number by dividing and averaging iteratively.</li>

93 </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>

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

95 <p>▶</p>

96 <h2>Jaskaran Singh Saluja</h2>

97 <h3>About the Author</h3>

98 <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>

99 <h3>Fun Fact</h3>

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