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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 8450.</p>

4 <h2>What is the Square Root of 8450?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 8450 is not a<a>perfect square</a>. The square root of 8450 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √8450, whereas (8450)^(1/2) in the exponential form. √8450 ≈ 91.9239, 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 8450</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 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 8450 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 8450 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 8450 Breaking it down, we get 2 x 5 x 5 x 13 x 13: 2^1 x 5^2 x 13^2</p>

14 <p><strong>Step 2:</strong>Now that we have found the prime factors of 8450, the second step is to make pairs of those prime factors. Since 8450 is not a perfect square, the digits of the number can’t be grouped completely into pairs. Therefore, calculating √8450 using prime factorization yields an approximate value.</p>

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17 <h2>Square Root of 8450 by Long Division Method</h2>

16 <h2>Square Root of 8450 by Long Division Method</h2>

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. Step 1: To begin with, we need to group the numbers from right to left. In the case of 8450, we need to group it as 50 and 84. Step 2: Now we need to find n whose square is closest to 84 without exceeding it. We can use n as ‘9’ because 9 x 9 = 81, which is<a>less than</a>84. Now the<a>quotient</a>is 9, and after subtracting 81 from 84, the<a>remainder</a>is 3. Step 3: Now let us bring down 50, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 9 + 9 = 18, which will be our new divisor. Step 4: The new divisor will be 18n. We need to find the value of n such that 18n x n <= 350. Let us consider n as 1. Now, 181 x 1 = 181. Step 5: Subtract 181 from 350, and the difference is 169. Step 6: 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 16900. Step 7: Now we need to find the new divisor that is 91 because 1891 x 9 = 17019. Step 8: Subtracting 17019 from 16900 gives us a result of -119, which indicates a small overestimate, so we adjust accordingly. Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero. So the square root of √8450 is approximately 91.92.</p>

17 <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. Step 1: To begin with, we need to group the numbers from right to left. In the case of 8450, we need to group it as 50 and 84. Step 2: Now we need to find n whose square is closest to 84 without exceeding it. We can use n as ‘9’ because 9 x 9 = 81, which is<a>less than</a>84. Now the<a>quotient</a>is 9, and after subtracting 81 from 84, the<a>remainder</a>is 3. Step 3: Now let us bring down 50, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 9 + 9 = 18, which will be our new divisor. Step 4: The new divisor will be 18n. We need to find the value of n such that 18n x n <= 350. Let us consider n as 1. Now, 181 x 1 = 181. Step 5: Subtract 181 from 350, and the difference is 169. Step 6: 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 16900. Step 7: Now we need to find the new divisor that is 91 because 1891 x 9 = 17019. Step 8: Subtracting 17019 from 16900 gives us a result of -119, which indicates a small overestimate, so we adjust accordingly. Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero. So the square root of √8450 is approximately 91.92.</p>

19 <h2>Square Root of 8450 by Approximation Method</h2>

18 <h2>Square Root of 8450 by Approximation Method</h2>

20 <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 8450 using the approximation method.</p>

19 <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 8450 using the approximation method.</p>

21 <p><strong>Step 1:</strong>We have to find the closest perfect squares to √8450. The smallest perfect square less than 8450 is 8281, and the largest perfect square less than 8450 is 8836. √8450 falls somewhere between 91 and 94.</p>

20 <p><strong>Step 1:</strong>We have to find the closest perfect squares to √8450. The smallest perfect square less than 8450 is 8281, and the largest perfect square less than 8450 is 8836. √8450 falls somewhere between 91 and 94.</p>

22 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>

21 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>

23 <p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>

22 <p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>

24 <p>Using the formula (8450 - 8281) / (8836 - 8281) ≈ 0.642, we identified the<a>decimal</a>point of our square root.</p>

23 <p>Using the formula (8450 - 8281) / (8836 - 8281) ≈ 0.642, we identified the<a>decimal</a>point of our square root.</p>

25 <p>The next step is adding the value we got initially to the decimal number, which is 91 + 0.92 = 91.92, so the square root of 8450 is approximately 91.92.</p>

24 <p>The next step is adding the value we got initially to the decimal number, which is 91 + 0.92 = 91.92, so the square root of 8450 is approximately 91.92.</p>

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 8450</h2>

25 <h2>Common Mistakes and How to Avoid Them in the Square Root of 8450</h2>

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

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

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28 <h3>Problem 1</h3>

29 <p>Can you help Max find the area of a square box if its side length is given as √8450?</p>

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

31 <p>The area of the square is approximately 8450 square units.</p>

32 <h3>Explanation</h3>

33 <p>The area of the square = side². The side length is given as √8450. Area of the square = side² = √8450 x √8450 = 8450. Therefore, the area of the square box is approximately 8450 square units.</p>

34 <p>Well explained 👍</p>

35 <h3>Problem 2</h3>

36 <p>A square-shaped building measuring 8450 square feet is built; if each of the sides is √8450, what will be the square feet of half of the building?</p>

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

38 <p>4225 square feet</p>

39 <h3>Explanation</h3>

40 <p>We can just divide the given area by 2 as the building is square-shaped. Dividing 8450 by 2, we get 4225. So half of the building measures 4225 square feet.</p>

41 <p>Well explained 👍</p>

42 <h3>Problem 3</h3>

43 <p>Calculate √8450 x 5.</p>

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

45 <p>Approximately 459.62</p>

46 <h3>Explanation</h3>

47 <p>The first step is to find the square root of 8450, which is approximately 91.92. The second step is to multiply 91.92 by 5. So 91.92 x 5 ≈ 459.62.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 4</h3>

50 <p>What will be the square root of (8450 + 50)?</p>

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

52 <p>The square root is approximately 92.</p>

53 <h3>Explanation</h3>

54 <p>To find the square root, we need to find the sum of (8450 + 50). 8450 + 50 = 8500, and then √8500 ≈ 92. Therefore, the square root of (8450 + 50) is approximately ±92.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 5</h3>

57 <p>Find the perimeter of the rectangle if its length ‘l’ is √8450 units and the width ‘w’ is 50 units.</p>

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

59 <p>The perimeter of the rectangle is approximately 283.84 units.</p>

60 <h3>Explanation</h3>

61 <p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√8450 + 50) = 2 × (91.92 + 50) = 2 × 141.92 ≈ 283.84 units.</p>

62 <p>Well explained 👍</p>

63 <h2>FAQ on Square Root of 8450</h2>

64 <h3>1.What is √8450 in its simplest form?</h3>

65 <p>The prime factorization of 8450 is 2 x 5 x 5 x 13 x 13, so the simplest form of √8450 = √(2 x 5^2 x 13^2).</p>

66 <h3>2.Mention the factors of 8450.</h3>

67 <p>Factors of 8450 include 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 169, 325, 338, 650, 845, 1690, 4225, and 8450.</p>

68 <h3>3.Calculate the square of 8450.</h3>

69 <p>We get the square of 8450 by multiplying the number by itself, that is 8450 x 8450 = 71402500.</p>

70 <h3>4.Is 8450 a prime number?</h3>

71 <p>8450 is not a<a>prime number</a>, as it has more than two factors.</p>

72 <h3>5.8450 is divisible by?</h3>

73 <p>8450 is divisible by several numbers, including 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 169, 325, 338, 650, 845, 1690, 4225, and 8450.</p>

74 <h2>Important Glossaries for the Square Root of 8450</h2>

75 <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>

76 <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>

77 <li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is more commonly used in real-world applications. This is known as the principal square root. </li>

78 <li><strong>Prime factorization:</strong>This is the process of expressing a number as the product of its prime factors, which is useful in finding square roots. </li>

79 <li><strong>Long division method:</strong>A method used to find the square root of a non-perfect square by dividing the number into groups and calculating step by step to achieve an approximate value.</li>

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

81 <p>▶</p>

82 <h2>Jaskaran Singh Saluja</h2>

83 <h3>About the Author</h3>

84 <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>

85 <h3>Fun Fact</h3>

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