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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, etc. Here, we will discuss the square root of 873.</p>

4 <h2>What is the Square Root of 873?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 873 is not a<a>perfect square</a>. The square root of 873 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √873, whereas (873)^(1/2) in the exponential form. √873 ≈ 29.542, 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 873</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>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 873 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 873 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 873</p>

14 <p>Breaking it down, we get 3 x 3 x 97: 3^2 x 97</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 873. The second step is to make pairs of those prime factors. Since 873 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating √873 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 873 by Long Division Method</h2>

17 <h2>Square Root of 873 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 873, we need to group it as 73 and 8.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 873, we need to group it as 73 and 8.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is 8. We can say n as ‘2’ because 2 x 2 is<a>less than</a>or equal to 8. Now the<a>quotient</a>is 2; after subtracting 4 from 8, the<a>remainder</a>is 4.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is 8. We can say n as ‘2’ because 2 x 2 is<a>less than</a>or equal to 8. Now the<a>quotient</a>is 2; after subtracting 4 from 8, the<a>remainder</a>is 4.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 73, which becomes the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 2 + 2, which gives us 4, our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 73, which becomes the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 2 + 2, which gives us 4, our new divisor.</p>

23 <p><strong>Step 4:</strong>Multiply the new divisor by a number m such that 4m x m ≤ 473. Let m be 7, then 47 x 7 = 329.</p>

22 <p><strong>Step 4:</strong>Multiply the new divisor by a number m such that 4m x m ≤ 473. Let m be 7, then 47 x 7 = 329.</p>

24 <p><strong>Step 5:</strong>Subtract 329 from 473; the difference is 144, and the quotient is 27.</p>

23 <p><strong>Step 5:</strong>Subtract 329 from 473; the difference is 144, and the quotient is 27.</p>

25 <p><strong>Step 6:</strong>Since the dividend is less than the 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 14400.</p>

24 <p><strong>Step 6:</strong>Since the dividend is less than the 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 14400.</p>

26 <p><strong>Step 7:</strong>Find a new divisor: 547. 547 x 2 = 1094</p>

25 <p><strong>Step 7:</strong>Find a new divisor: 547. 547 x 2 = 1094</p>

27 <p><strong>Step 8:</strong>Subtracting 1094 from 14400 gives us 13306.</p>

26 <p><strong>Step 8:</strong>Subtracting 1094 from 14400 gives us 13306.</p>

28 <p><strong>Step 9:</strong>Continue doing these steps until we get two decimal places.</p>

27 <p><strong>Step 9:</strong>Continue doing these steps until we get two decimal places.</p>

29 <p>So the square root of √873 is approximately 29.54.</p>

28 <p>So the square root of √873 is approximately 29.54.</p>

30 <h2>Square Root of 873 by Approximation Method</h2>

29 <h2>Square Root of 873 by Approximation Method</h2>

31 <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 873 using the approximation method.</p>

30 <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 873 using the approximation method.</p>

32 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √873. The smallest perfect square less than 873 is 841, and the largest perfect square<a>greater than</a>873 is 900. √873 falls somewhere between 29 and 30.</p>

31 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √873. The smallest perfect square less than 873 is 841, and the largest perfect square<a>greater than</a>873 is 900. √873 falls somewhere between 29 and 30.</p>

33 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>

32 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>

34 <p>Using the formula: (873 - 841) / (900 - 841) = 0.542 The next step is adding the initial<a>whole number</a>to the<a>decimal</a>value, which is 29 + 0.542 = 29.542. Therefore, the square root of 873 is approximately 29.542.</p>

33 <p>Using the formula: (873 - 841) / (900 - 841) = 0.542 The next step is adding the initial<a>whole number</a>to the<a>decimal</a>value, which is 29 + 0.542 = 29.542. Therefore, the square root of 873 is approximately 29.542.</p>

35 <h2>Common Mistakes and How to Avoid Them in the Square Root of 873</h2>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 873</h2>

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

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

36 + <h2>Download Worksheets</h2>

37 <h3>Problem 1</h3>

38 <p>Can you help Max find the area of a square box if its side length is given as √783?</p>

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

40 <p>The area of the square is approximately 783 square units.</p>

41 <h3>Explanation</h3>

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

43 <p>The side length is given as √783.</p>

44 <p>Area of the square = side² = √783 x √783 = 783.</p>

45 <p>Therefore, the area of the square box is approximately 783 square units.</p>

46 <p>Well explained 👍</p>

47 <h3>Problem 2</h3>

48 <p>A square-shaped building measuring 873 square feet is built. If each of the sides is √873, what will be the square feet of half of the building?</p>

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

50 <p>436.5 square feet</p>

51 <h3>Explanation</h3>

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

53 <p>Dividing 873 by 2 gives us 436.5.</p>

54 <p>So, half of the building measures 436.5 square feet.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 3</h3>

57 <p>Calculate √873 x 5.</p>

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

59 <p>Approximately 147.71</p>

60 <h3>Explanation</h3>

61 <p>The first step is to find the square root of 873, which is approximately 29.54.</p>

62 <p>The second step is to multiply 29.54 by 5.</p>

63 <p>So, 29.54 x 5 ≈ 147.71.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

66 <p>What will be the square root of (873 + 27)?</p>

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

68 <p>The square root is 30.</p>

69 <h3>Explanation</h3>

70 <p>To find the square root, we need to find the sum of (873 + 27). 873 + 27 = 900, and √900 = 30.</p>

71 <p>Therefore, the square root of (873 + 27) is ±30.</p>

72 <p>Well explained 👍</p>

73 <h3>Problem 5</h3>

74 <p>Find the perimeter of the rectangle if its length ‘l’ is √783 units and the width ‘w’ is 38 units.</p>

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

76 <p>The perimeter of the rectangle is approximately 118.08 units.</p>

77 <h3>Explanation</h3>

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

79 <p>Perimeter = 2 × (√783 + 38) = 2 × (27.97 + 38) ≈ 2 × 65.97 ≈ 131.94 units.</p>

80 <p>Well explained 👍</p>

81 <h2>FAQ on Square Root of 873</h2>

82 <h3>1.What is √873 in its simplest form?</h3>

83 <p>The prime factorization of 873 is 3 x 3 x 97, so the simplest form of √873 = √(3 x 3 x 97).</p>

84 <h3>2.Mention the factors of 873.</h3>

85 <p>Factors of 873 are 1, 3, 9, 97, 291, and 873.</p>

86 <h3>3.Calculate the square of 873.</h3>

87 <p>We get the square of 873 by multiplying the number by itself, that is 873 x 873 = 761,529.</p>

88 <h3>4.Is 873 a prime number?</h3>

89 <h3>5.873 is divisible by?</h3>

90 <p>873 has several factors; those are 1, 3, 9, 97, 291, and 873.</p>

91 <h2>Important Glossaries for the Square Root of 873</h2>

92 <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, which is √16 = 4. </li>

93 <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>

94 <li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is more commonly used due to its real-world applications. Hence, it is known as the principal square root. </li>

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

96 <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>

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

98 <p>▶</p>

99 <h2>Jaskaran Singh Saluja</h2>

100 <h3>About the Author</h3>

101 <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>

102 <h3>Fun Fact</h3>

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