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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 like engineering, finance, etc. Here, we will discuss the square root of 1045.</p>

4 <h2>What is the Square Root of 1045?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1045 is not a<a>perfect square</a>. The square root of 1045 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1045, whereas (1045)^(1/2) in exponential form. √1045 ≈ 32.343, 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 1045</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<a>long division</a>and approximation methods 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 1045 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 1045 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1045 Breaking it down, we get 5 × 11 × 19.</p>

14 <p><strong>Step 2:</strong>We found the prime factors of 1045. Since 1045 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>

15 <p>Therefore, calculating √1045 using prime factorization directly is not possible.</p>

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18 <h2>Square Root of 1045 by Long Division Method</h2>

17 <h2>Square Root of 1045 by Long Division Method</h2>

19 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. 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. 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, group the numbers from right to left. In the case of 1045, we need to group it as 10 and 45.</p>

19 <p><strong>Step 1:</strong>To begin, group the numbers from right to left. In the case of 1045, we need to group it as 10 and 45.</p>

21 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 10. We can say this number is ‘3’ because 3 × 3 = 9. The<a>quotient</a>is 3, and the<a>remainder</a>is 1 after subtracting 9 from 10.</p>

20 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 10. We can say this number is ‘3’ because 3 × 3 = 9. The<a>quotient</a>is 3, and the<a>remainder</a>is 1 after subtracting 9 from 10.</p>

22 <p><strong>Step 3:</strong>Bring down the next pair, which is 45, making the new<a>dividend</a>145. Add the old<a>divisor</a>with the same number, 3 + 3 = 6, to get the new divisor.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair, which is 45, making the new<a>dividend</a>145. Add the old<a>divisor</a>with the same number, 3 + 3 = 6, to get the new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor will be 6n. Find the largest value of n such that 6n × n ≤ 145. The value n is 2, so 62 × 2 = 124.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 6n. Find the largest value of n such that 6n × n ≤ 145. The value n is 2, so 62 × 2 = 124.</p>

24 <p><strong>Step 5:</strong>Subtract 124 from 145, the result is 21, and the quotient is 32.</p>

23 <p><strong>Step 5:</strong>Subtract 124 from 145, the result is 21, and the quotient is 32.</p>

25 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point. Add two zeroes to the dividend to make it 2100.</p>

24 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point. Add two zeroes to the dividend to make it 2100.</p>

26 <p><strong>Step 7:</strong>The new divisor is 644. Find a number n such that 644n × n is less than or equal to 2100. Continue this process to achieve better precision.</p>

25 <p><strong>Step 7:</strong>The new divisor is 644. Find a number n such that 644n × n is less than or equal to 2100. Continue this process to achieve better precision.</p>

27 <p>So, the square root of √1045 is approximately 32.343.</p>

26 <p>So, the square root of √1045 is approximately 32.343.</p>

28 <h2>Square Root of 1045 by Approximation Method</h2>

27 <h2>Square Root of 1045 by Approximation Method</h2>

29 <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 1045 using the approximation method.</p>

28 <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 1045 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Find the closest perfect squares of √1045. The smallest perfect square less than 1045 is 1024 (32^2), and the largest perfect square<a>greater than</a>1045 is 1089 (33^2). √1045 falls between 32 and 33.</p>

29 <p><strong>Step 1:</strong>Find the closest perfect squares of √1045. The smallest perfect square less than 1045 is 1024 (32^2), and the largest perfect square<a>greater than</a>1045 is 1089 (33^2). √1045 falls between 32 and 33.</p>

31 <p><strong>Step 2:</strong>Apply the approximation<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using (1045 - 1024) / (1089 - 1024) = 21 / 65 = 0.323.</p>

30 <p><strong>Step 2:</strong>Apply the approximation<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using (1045 - 1024) / (1089 - 1024) = 21 / 65 = 0.323.</p>

32 <p>The approximate square root is 32 + 0.323 = 32.323.</p>

31 <p>The approximate square root is 32 + 0.323 = 32.323.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1045</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1045</h2>

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

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

34 + <h2>Download Worksheets</h2>

35 <h3>Problem 1</h3>

36 <p>Can you help Max find the area of a square box if its side length is given as √1045?</p>

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

38 <p>The area of the square is approximately 1045 square units.</p>

39 <h3>Explanation</h3>

40 <p>The area of a square = side^2.</p>

41 <p>The side length is given as √1045.</p>

42 <p>Area = (√1045) × (√1045) = 1045.</p>

43 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

45 <p>A square-shaped building measuring 1045 square feet is built; if each side is √1045, what will be the square feet of half of the building?</p>

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

47 <p>522.5 square feet</p>

48 <h3>Explanation</h3>

49 <p>Divide the total area by 2 since the building is square-shaped.</p>

50 <p>1045 / 2 = 522.5 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √1045 × 3.</p>

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

55 <p>Approximately 97.029</p>

56 <h3>Explanation</h3>

57 <p>First, find the square root of 1045, which is approximately 32.343. Then multiply 32.343 by 3: 32.343 × 3 ≈ 97.029.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

60 <p>What will be the square root of (1024 + 21)?</p>

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

62 <p>The square root is 33.</p>

63 <h3>Explanation</h3>

64 <p>Find the sum of (1024 + 21) = 1045, then find the square root of 1045, which is approximately 32.343, but since this is a sum leading to a perfect square (1089), it simplifies to 33.</p>

65 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

67 <p>Find the perimeter of a rectangle if its length ‘l’ is √1045 units and the width ‘w’ is 25 units.</p>

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

69 <p>The perimeter of the rectangle is approximately 114.686 units.</p>

70 <h3>Explanation</h3>

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

72 <p>Perimeter = 2 × (√1045 + 25)</p>

73 <p>= 2 × (32.343 + 25)</p>

74 <p>≈ 114.686 units.</p>

75 <p>Well explained 👍</p>

76 <h2>FAQ on Square Root of 1045</h2>

77 <h3>1.What is √1045 in its simplest form?</h3>

78 <p>The prime factorization of 1045 is 5 × 11 × 19, so the simplest form of √1045 cannot be further simplified into a perfect square factor form.</p>

79 <h3>2.Mention the factors of 1045.</h3>

80 <p>Factors of 1045 are 1, 5, 11, 19, 55, 95, 209, and 1045.</p>

81 <h3>3.Calculate the square of 1045.</h3>

82 <p>The square of 1045 is 1045 × 1045 = 1,092,025.</p>

83 <h3>4.Is 1045 a prime number?</h3>

84 <p>1045 is not a<a>prime number</a>, as it has more than two factors.</p>

85 <h3>5.1045 is divisible by?</h3>

86 <p>1045 is divisible by 1, 5, 11, 19, 55, 95, 209, and 1045.</p>

87 <h2>Important Glossaries for the Square Root of 1045</h2>

88 <ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, if 4^2 = 16, then √16 = 4. </li>

89 <li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal expansion. </li>

90 <li><strong>Principal square root:</strong>The non-negative square root of a number. For example, the principal square root of 25 is 5. </li>

91 <li><strong>Factors:</strong>Numbers you can multiply together to get another number. For example, factors of 12 are 1, 2, 3, 4, 6, and 12. </li>

92 <li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.</li>

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

94 <p>▶</p>

95 <h2>Jaskaran Singh Saluja</h2>

96 <h3>About the Author</h3>

97 <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>

98 <h3>Fun Fact</h3>

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