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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 fields of mathematics, engineering, and science. Here, we will discuss the square root of 3.25.</p>

4 <h2>What is the Square Root of 3.25?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 3.25 is not a<a>perfect square</a>. The square root of 3.25 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √3.25, whereas (3.25)^(1/2) in the exponential form. √3.25 ≈ 1.80278, 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 3.25</h2>

7 <p>The<a>prime factorization</a>method is more suitable for perfect square numbers. However, for non-perfect square numbers like 3.25, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>

8 <ul><li>Long division method</li>

9 <li>Approximation method</li>

10 </ul><h2>Square Root of 3.25 by Long Division Method</h2>

11 <p>The<a>long division</a>method is particularly effective for non-perfect square numbers. In this method, we focus on finding the<a>square root</a>through a<a>series</a>of steps.</p>

12 <p><strong>Step 1:</strong>To begin,<a>set</a>the number 3.25 in<a>decimal</a>form and consider it as 325.</p>

13 <p><strong>Step 2:</strong>Pair the digits starting from the decimal point. In this case, we have 3.25, so the pair is 32 and 5.</p>

14 <p><strong>Step 3:</strong>Find a number whose square is<a>less than</a>or equal to 3. The number is 1 because 1 × 1 ≤ 3.</p>

15 <p><strong>Step 4:</strong>Subtract 1² from 3 to get the<a>remainder</a>2, and bring down 2 to make it 22.</p>

16 <p><strong>Step 5:</strong>Double the divisor (1) to get 2 and find a digit to append to 2 to make it less than or equal to 225. That digit is 8 because 28 × 8 = 224.</p>

17 <p><strong>Step 6:</strong>Subtract 224 from 225 to get the remainder 1. Bring down 00 to make it 100.</p>

18 <p><strong>Step 7:</strong>Double the divisor 18 to get 36 and determine a digit to append to 36 to make it less than or equal to 100. That digit is 2 because 362 × 2 = 724.</p>

19 <p><strong>Step 8:</strong>Continue this process until the desired precision is achieved.</p>

20 <p>The result is approximately 1.80278.</p>

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23 <h2>Square Root of 3.25 by Approximation Method</h2>

22 <h2>Square Root of 3.25 by Approximation Method</h2>

24 <p>The approximation method is another approach for finding square roots. It involves estimating the value based on nearby perfect squares.</p>

23 <p>The approximation method is another approach for finding square roots. It involves estimating the value based on nearby perfect squares.</p>

25 <p><strong>Step 1:</strong>Identify the nearest perfect squares surrounding 3.25. The closest perfect squares are 1 (1²) and 4 (2²), so √3.25 is between 1 and 2.</p>

24 <p><strong>Step 1:</strong>Identify the nearest perfect squares surrounding 3.25. The closest perfect squares are 1 (1²) and 4 (2²), so √3.25 is between 1 and 2.</p>

26 <p><strong>Step 2:</strong>Use interpolation to approximate the value. Given that 3.25 is closer to 4 than to 1, we can estimate the square root is closer to 2.</p>

25 <p><strong>Step 2:</strong>Use interpolation to approximate the value. Given that 3.25 is closer to 4 than to 1, we can estimate the square root is closer to 2.</p>

27 <p><strong>Step 3:</strong>Using the<a>formula</a>(Given number - smaller perfect square) / (Larger perfect square - smaller perfect square), we get: (3.25 - 1) / (4 - 1) = 2.25 / 3 ≈ 0.75</p>

26 <p><strong>Step 3:</strong>Using the<a>formula</a>(Given number - smaller perfect square) / (Larger perfect square - smaller perfect square), we get: (3.25 - 1) / (4 - 1) = 2.25 / 3 ≈ 0.75</p>

28 <p><strong>Step 4:</strong>Adding this to the lower boundary value gives us 1 + 0.75 = 1.75.</p>

27 <p><strong>Step 4:</strong>Adding this to the lower boundary value gives us 1 + 0.75 = 1.75.</p>

29 <p>Adjusting through trial and error, we find that √3.25 ≈ 1.80278.</p>

28 <p>Adjusting through trial and error, we find that √3.25 ≈ 1.80278.</p>

30 <h2>Mistakes in Calculating the Square Root of 3.25</h2>

29 <h2>Mistakes in Calculating the Square Root of 3.25</h2>

31 <p>When calculating the square root, students might make errors such as omitting the negative square root or misplacing the decimal point. Let's explore some common mistakes in detail.</p>

30 <p>When calculating the square root, students might make errors such as omitting the negative square root or misplacing the decimal point. Let's explore some common mistakes in detail.</p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>Can you help Max find the area of a square box if its side length is given as √3.25?</p>

32 <p>Can you help Max find the area of a square box if its side length is given as √3.25?</p>

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

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

35 <p>The area of the square is approximately 10.5601 square units.</p>

34 <p>The area of the square is approximately 10.5601 square units.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

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

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

38 <p>The side length is given as √3.25 ≈ 1.80278.</p>

37 <p>The side length is given as √3.25 ≈ 1.80278.</p>

39 <p>Area = (√3.25)² = 1.80278 × 1.80278 ≈ 3.25.</p>

38 <p>Area = (√3.25)² = 1.80278 × 1.80278 ≈ 3.25.</p>

40 <p>Therefore, the area of the square box is approximately 3.25 square units.</p>

39 <p>Therefore, the area of the square box is approximately 3.25 square units.</p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

41 <h3>Problem 2</h3>

43 <p>A square-shaped garden measuring 3.25 square meters is built; if each of the sides is √3.25, what will be the square meters of half of the garden?</p>

42 <p>A square-shaped garden measuring 3.25 square meters is built; if each of the sides is √3.25, what will be the square meters of half of the garden?</p>

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

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

45 <p>1.625 square meters</p>

44 <p>1.625 square meters</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>We can divide the given area by 2 since the garden is square-shaped.</p>

46 <p>We can divide the given area by 2 since the garden is square-shaped.</p>

48 <p>Dividing 3.25 by 2, we get 1.625.</p>

47 <p>Dividing 3.25 by 2, we get 1.625.</p>

49 <p>So, half of the garden measures 1.625 square meters.</p>

48 <p>So, half of the garden measures 1.625 square meters.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>Calculate √3.25 × 5.</p>

51 <p>Calculate √3.25 × 5.</p>

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

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

54 <p>Approximately 9.0139</p>

53 <p>Approximately 9.0139</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>First, find the square root of 3.25, which is approximately 1.80278.</p>

55 <p>First, find the square root of 3.25, which is approximately 1.80278.</p>

57 <p>Then, multiply 1.80278 by 5.</p>

56 <p>Then, multiply 1.80278 by 5.</p>

58 <p>So 1.80278 × 5 ≈ 9.0139.</p>

57 <p>So 1.80278 × 5 ≈ 9.0139.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 4</h3>

59 <h3>Problem 4</h3>

61 <p>What will be the square root of (2 + 1.25)?</p>

60 <p>What will be the square root of (2 + 1.25)?</p>

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

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

63 <p>The square root is approximately 1.80278.</p>

62 <p>The square root is approximately 1.80278.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

65 <p>To find the square root, we compute the sum of (2 + 1.25), which totals 3.25. √3.25 ≈ 1.80278.</p>

64 <p>To find the square root, we compute the sum of (2 + 1.25), which totals 3.25. √3.25 ≈ 1.80278.</p>

66 <p>Therefore, the square root of (2 + 1.25) is approximately 1.80278.</p>

65 <p>Therefore, the square root of (2 + 1.25) is approximately 1.80278.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

67 <h3>Problem 5</h3>

69 <p>Find the perimeter of the rectangle if its length ‘l’ is √3.25 units and the width ‘w’ is 5 units.</p>

68 <p>Find the perimeter of the rectangle if its length ‘l’ is √3.25 units and the width ‘w’ is 5 units.</p>

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

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

71 <p>The perimeter of the rectangle is approximately 13.6056 units.</p>

70 <p>The perimeter of the rectangle is approximately 13.6056 units.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

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

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

74 <p>Perimeter = 2 × (√3.25 + 5) ≈ 2 × (1.80278 + 5) ≈ 2 × 6.80278 ≈ 13.6056 units.</p>

73 <p>Perimeter = 2 × (√3.25 + 5) ≈ 2 × (1.80278 + 5) ≈ 2 × 6.80278 ≈ 13.6056 units.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h2>FAQ on Square Root of 3.25</h2>

75 <h2>FAQ on Square Root of 3.25</h2>

77 <h3>1.What is √3.25 in its simplest form?</h3>

76 <h3>1.What is √3.25 in its simplest form?</h3>

78 <p>The simplest form of √3.25 is an approximation, as 3.25 is not a perfect square. Thus, √3.25 ≈ 1.80278.</p>

77 <p>The simplest form of √3.25 is an approximation, as 3.25 is not a perfect square. Thus, √3.25 ≈ 1.80278.</p>

79 <h3>2.Is 3.25 a perfect square?</h3>

78 <h3>2.Is 3.25 a perfect square?</h3>

80 <p>No, 3.25 is not a perfect square because it cannot be expressed as the square of an integer.</p>

79 <p>No, 3.25 is not a perfect square because it cannot be expressed as the square of an integer.</p>

81 <h3>3.Calculate the square of 3.25.</h3>

80 <h3>3.Calculate the square of 3.25.</h3>

82 <p>To find the square of 3.25, multiply the number by itself, which is 3.25 × 3.25 = 10.5625.</p>

81 <p>To find the square of 3.25, multiply the number by itself, which is 3.25 × 3.25 = 10.5625.</p>

83 <h3>4.Is 3.25 a rational number?</h3>

82 <h3>4.Is 3.25 a rational number?</h3>

84 <h3>5.What is the decimal expansion of √3.25?</h3>

83 <h3>5.What is the decimal expansion of √3.25?</h3>

85 <p>The decimal expansion of √3.25 is approximately 1.80278, and it is non-repeating and non-terminating, making it an irrational number.</p>

84 <p>The decimal expansion of √3.25 is approximately 1.80278, and it is non-repeating and non-terminating, making it an irrational number.</p>

86 <h2>Important Glossaries for the Square Root of 3.25</h2>

85 <h2>Important Glossaries for the Square Root of 3.25</h2>

87 <ul><li><strong>Square root:</strong>A square root is a number that, when multiplied by itself, gives the original number. Example: √9 = 3.</li>

86 <ul><li><strong>Square root:</strong>A square root is a number that, when multiplied by itself, gives the original number. Example: √9 = 3.</li>

88 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. Its decimal expansion is non-repeating and non-terminating</li>

87 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. Its decimal expansion is non-repeating and non-terminating</li>

89 </ul><ul><li><strong>Approximation:</strong>An approximation is an estimated value close to the actual value. Often used for irrational numbers.</li>

88 </ul><ul><li><strong>Approximation:</strong>An approximation is an estimated value close to the actual value. Often used for irrational numbers.</li>

90 </ul><ul><li><strong>Decimal:</strong>A decimal represents a fraction using powers of ten, such as 0.5 or 3.25.</li>

89 </ul><ul><li><strong>Decimal:</strong>A decimal represents a fraction using powers of ten, such as 0.5 or 3.25.</li>

91 </ul><ul><li><strong>Long division method:</strong>A technique used for finding square roots of non-perfect squares by dividing the number into pairs of digits and estimating step by step.</li>

90 </ul><ul><li><strong>Long division method:</strong>A technique used for finding square roots of non-perfect squares by dividing the number into pairs of digits and estimating step by step.</li>

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

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

93 <p>▶</p>

92 <p>▶</p>

94 <h2>Jaskaran Singh Saluja</h2>

93 <h2>Jaskaran Singh Saluja</h2>

95 <h3>About the Author</h3>

94 <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>

95 <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>

96 <h3>Fun Fact</h3>

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

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