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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 4761.</p>

4 <h2>What is the Square Root of 4761?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4761 is a<a>perfect square</a>. The square root of 4761 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4761, whereas (4761)^(1/2) in the exponential form. √4761 = 69, which is a<a>rational number</a>because it can 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 4761</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. Since 4761 is a perfect square, we can use the prime factorization method to find its<a>square root</a>. Other methods, such as the<a>long division</a>method and approximation method, can also be 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 4761 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 4761 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 4761</p>

14 <p>Breaking it down, we get 3 x 3 x 23 x 23: 3² x 23²</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 4761. The second step is to make pairs of those prime factors. Since 4761 is a perfect square, the digits of the number can be grouped into pairs. Therefore, √4761 = 3 x 23 = 69.</p>

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18 <h2>Square Root of 4761 by Long Division Method</h2>

17 <h2>Square Root of 4761 by Long Division Method</h2>

19 <p>The long<a>division</a>method is particularly used for perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step:</p>

18 <p>The long<a>division</a>method is particularly used for perfect and non-perfect square numbers. Let us now learn how to find the square root 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 4761, we need to group it as 47 and 61.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 4761, we need to group it as 47 and 61.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 47. We can say n is 6 because 6 x 6 = 36, which is less than 47. The<a>quotient</a>is 6, and the<a>remainder</a>is 47 - 36 = 11.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 47. We can say n is 6 because 6 x 6 = 36, which is less than 47. The<a>quotient</a>is 6, and the<a>remainder</a>is 47 - 36 = 11.</p>

22 <p><strong>Step 3:</strong>Bring down 61 to make the new<a>dividend</a>1161. Double the quotient (6) to get 12, which will be our new<a>divisor</a>.</p>

21 <p><strong>Step 3:</strong>Bring down 61 to make the new<a>dividend</a>1161. Double the quotient (6) to get 12, which will be our new<a>divisor</a>.</p>

23 <p><strong>Step 4:</strong>Find a digit m such that 12m x m is less than or equal to 1161. We find that m is 9 because 129 x 9 = 1161.</p>

22 <p><strong>Step 4:</strong>Find a digit m such that 12m x m is less than or equal to 1161. We find that m is 9 because 129 x 9 = 1161.</p>

24 <p><strong>Step 5:</strong>Since there is no remainder, the quotient is 69. Therefore, the square root of 4761 is 69.</p>

23 <p><strong>Step 5:</strong>Since there is no remainder, the quotient is 69. Therefore, the square root of 4761 is 69.</p>

25 <h2>Square Root of 4761 by Approximation Method</h2>

24 <h2>Square Root of 4761 by Approximation Method</h2>

26 <p>The approximation method can be used to confirm the square root of a number. Since 4761 is a perfect square, approximation will confirm the result:</p>

25 <p>The approximation method can be used to confirm the square root of a number. Since 4761 is a perfect square, approximation will confirm the result:</p>

27 <p><strong>Step 1:</strong>We know that 4761 is between 3600 (60²) and 4900 (70²). Therefore, √4761 falls between 60 and 70.</p>

26 <p><strong>Step 1:</strong>We know that 4761 is between 3600 (60²) and 4900 (70²). Therefore, √4761 falls between 60 and 70.</p>

28 <p><strong>Step 2:</strong>Calculate the midpoint: (60 + 70) / 2 = 65. Test squares around this point. Step 3: We find that 69 x 69 = 4761, confirming that the square root of 4761 is 69.</p>

27 <p><strong>Step 2:</strong>Calculate the midpoint: (60 + 70) / 2 = 65. Test squares around this point. Step 3: We find that 69 x 69 = 4761, confirming that the square root of 4761 is 69.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4761</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4761</h2>

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

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

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31 <h3>Problem 1</h3>

32 <p>Can you help Max find the area of a square box if its side length is given as √4761?</p>

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

34 <p>The area of the square is 4761 square units.</p>

35 <h3>Explanation</h3>

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

37 <p>The side length is given as √4761.</p>

38 <p>Area of the square = side² = √4761 x √4761 = 69 x 69 = 4761.</p>

39 <p>Therefore, the area of the square box is 4761 square units.</p>

40 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

42 <p>A square-shaped building measuring 4761 square feet is built; if each of the sides is √4761, what will be the square feet of half of the building?</p>

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

44 <p>2380.5 square feet</p>

45 <h3>Explanation</h3>

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

47 <p>Dividing 4761 by 2, we get 2380.5.</p>

48 <p>So, half of the building measures 2380.5 square feet.</p>

49 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

51 <p>Calculate √4761 x 5.</p>

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

53 <p>345</p>

54 <h3>Explanation</h3>

55 <p>The first step is to find the square root of 4761, which is 69.</p>

56 <p>The second step is to multiply 69 by 5.</p>

57 <p>So, 69 x 5 = 345.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

60 <p>What will be the square root of (4624 + 137)?</p>

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

62 <p>The square root is 70.</p>

63 <h3>Explanation</h3>

64 <p>To find the square root, we need to find the sum of (4624 + 137). 4624 + 137 = 4761, and then √4761 = 69.</p>

65 <p>Therefore, the square root of (4624 + 137) is ±69.</p>

66 <p>Well explained 👍</p>

67 <h3>Problem 5</h3>

68 <p>Find the perimeter of the rectangle if its length 'l' is √4761 units and the width 'w' is 38 units.</p>

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

70 <p>We find the perimeter of the rectangle as 214 units.</p>

71 <h3>Explanation</h3>

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

73 <p>Perimeter = 2 × (√4761 + 38) = 2 × (69 + 38) = 2 × 107 = 214 units.</p>

74 <p>Well explained 👍</p>

75 <h2>FAQ on Square Root of 4761</h2>

76 <h3>1.What is √4761 in its simplest form?</h3>

77 <p>The prime factorization of 4761 is 3 x 3 x 23 x 23, so the simplest form of √4761 = √(3² x 23²) = 69.</p>

78 <h3>2.Mention the factors of 4761.</h3>

79 <p>Factors of 4761 are 1, 3, 9, 23, 69, 207, 529, 1587, and 4761.</p>

80 <h3>3.Calculate the square of 69.</h3>

81 <p>We get the square of 69 by multiplying the number by itself, that is 69 x 69 = 4761.</p>

82 <h3>4.Is 4761 a prime number?</h3>

83 <p>4761 is not a<a>prime number</a>, as it has more than two factors.</p>

84 <h3>5.4761 is divisible by?</h3>

85 <p>4761 has many factors; those are 1, 3, 9, 23, 69, 207, 529, 1587, and 4761.</p>

86 <h2>Important Glossaries for the Square Root of 4761</h2>

87 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 8² = 64, and the inverse of the square is the square root, that is √64 = 8.</li>

88 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can 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>Perfect square:</strong>A perfect square is a number that is the square of an integer. Example: 64 is a perfect square of 8.</li>

90 </ul><ul><li><strong>Prime factorization</strong>: The expression of a number as a product of its prime factors. Example: The prime factorization of 18 is 2 x 3 x 3.</li>

91 </ul><ul><li><strong>Integer:</strong>An integer is a whole number that can be positive, negative, or zero. Example: -2, 0, 3, 42 are integers.</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>