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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 3375.</p>

4 <h2>What is the Square Root of 3375?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 3375 is not a<a>perfect square</a>. The square root of 3375 can be expressed in both radical and exponential forms. In radical form, it is expressed as √3375, whereas in<a>exponential form</a>it is expressed as (3375)^(1/2). √3375 = 58.09475, 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 3375</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><h3>Square Root of 3375 by Prime Factorization Method</h3>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 3375 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 3375 Breaking it down, we get 3 x 3 x 3 x 3 x 5 x 5 x 5:<a>3^4</a>x 5^3</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 3375. The second step is to make pairs of those prime factors. Since 3375 is not a perfect square, the digits of the number can’t be grouped in equal pairs. Therefore, calculating 3375 using prime factorization directly is complex.</p>

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17 <h3>Square Root of 3375 by Long Division Method</h3>

16 <h3>Square Root of 3375 by Long Division Method</h3>

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>

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.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 3375, we need to group it as 75 and 33.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 3375, we need to group it as 75 and 33.</p>

20 <p><strong>Step 2:</strong>Now we need to find a number whose square is<a>less than</a>or equal to 33. We can say this number is '5' because 5 x 5 = 25, which is less than 33. After subtracting, the<a>remainder</a>is 8.</p>

19 <p><strong>Step 2:</strong>Now we need to find a number whose square is<a>less than</a>or equal to 33. We can say this number is '5' because 5 x 5 = 25, which is less than 33. After subtracting, the<a>remainder</a>is 8.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 75, making it the new<a>dividend</a>. Add the previous<a>divisor</a>with itself, 5 + 5, which results in 10, our new divisor.</p>

20 <p><strong>Step 3:</strong>Now let us bring down 75, making it the new<a>dividend</a>. Add the previous<a>divisor</a>with itself, 5 + 5, which results in 10, our new divisor.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 10n where n is such that 10n x n is less than or equal to 875. We find n = 8, as 10 x 8 x 8 = 800.</p>

21 <p><strong>Step 4:</strong>The new divisor will be 10n where n is such that 10n x n is less than or equal to 875. We find n = 8, as 10 x 8 x 8 = 800.</p>

23 <p><strong>Step 5:</strong>Subtract 800 from 875, the remainder is 75. The<a>quotient</a>is now 58.</p>

22 <p><strong>Step 5:</strong>Subtract 800 from 875, the remainder is 75. The<a>quotient</a>is now 58.</p>

24 <p><strong>Step 6:</strong>Since the remainder is still present, add a decimal point and bring down two zeros, making the dividend 7500.</p>

23 <p><strong>Step 6:</strong>Since the remainder is still present, add a decimal point and bring down two zeros, making the dividend 7500.</p>

25 <p><strong>Step 7:</strong>The new divisor is 116, because 1168 x 8 = 9344, continuing this process until the desired decimal places are reached. So the square root of √3375 is approximately 58.094.</p>

24 <p><strong>Step 7:</strong>The new divisor is 116, because 1168 x 8 = 9344, continuing this process until the desired decimal places are reached. So the square root of √3375 is approximately 58.094.</p>

26 <h3>Square Root of 3375 by Approximation Method</h3>

25 <h3>Square Root of 3375 by Approximation Method</h3>

27 <p>The approximation method is useful for finding square roots easily. Let us learn how to find the square root of 3375 using the approximation method.</p>

26 <p>The approximation method is useful for finding square roots easily. Let us learn how to find the square root of 3375 using the approximation method.</p>

28 <p><strong>Step 1:</strong>Find the closest perfect squares to √3375. The largest perfect square smaller than 3375 is 3249, and the smallest perfect square larger than 3375 is 3481. √3375 falls between 57 and 59.</p>

27 <p><strong>Step 1:</strong>Find the closest perfect squares to √3375. The largest perfect square smaller than 3375 is 3249, and the smallest perfect square larger than 3375 is 3481. √3375 falls between 57 and 59.</p>

29 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square) Using the formula: (3375 - 3249) / (3481 - 3249) = 0.126 Add this<a>decimal</a>to the smaller estimate: 57 + 0.126 = 57.126, so the approximate square root of 3375 is 58.094.</p>

28 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square) Using the formula: (3375 - 3249) / (3481 - 3249) = 0.126 Add this<a>decimal</a>to the smaller estimate: 57 + 0.126 = 57.126, so the approximate square root of 3375 is 58.094.</p>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3375</h2>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3375</h2>

31 <p>Students often make mistakes in finding square roots, such as forgetting the negative square root, skipping steps in the long division method, etc. Let's look at a few common mistakes and how to avoid them.</p>

30 <p>Students often make mistakes in finding square roots, such as forgetting the negative square root, skipping steps in the long division method, etc. Let's look at a few common mistakes and how to avoid them.</p>

31 + <h2>Download Worksheets</h2>

32 <h3>Problem 1</h3>

33 <p>Can you help Max find the area of a square box if its side length is given as √3375?</p>

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

35 <p>The area of the square is approximately 3375 square units.</p>

36 <h3>Explanation</h3>

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

38 <p>The side length is given as √3375.</p>

39 <p>Area = (√3375) x (√3375) = 3375.</p>

40 <p>Therefore, the area of the square box is 3375 square units.</p>

41 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

43 <p>A square-shaped building measuring 3375 square feet is built; if each of the sides is √3375, what will be the square feet of half of the building?</p>

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

45 <p>1687.5 square feet</p>

46 <h3>Explanation</h3>

47 <p>Divide the given area by 2 as the building is square-shaped. Dividing 3375 by 2 gives 1687.5. So half of the building measures 1687.5 square feet.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

50 <p>Calculate √3375 x 5.</p>

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

52 <p>Approximately 290.47</p>

53 <h3>Explanation</h3>

54 <p>First, find the square root of 3375, which is approximately 58.094. Then, multiply 58.094 by 5. So, 58.094 x 5 = approximately 290.47.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

57 <p>What will be the square root of (3375 + 25)?</p>

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

59 <p>The square root is approximately 59.16</p>

60 <h3>Explanation</h3>

61 <p>To find the square root, first find the sum: 3375 + 25 = 3400. Then, calculate √3400, which is approximately 58.30952.</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 5</h3>

64 <p>Find the perimeter of the rectangle if its length ‘l’ is √3375 units and the width ‘w’ is 50 units.</p>

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

66 <p>The perimeter of the rectangle is approximately 216.188 units.</p>

67 <h3>Explanation</h3>

68 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3375 + 50) = 2 × (58.094 + 50) = 2 × 108.094 = approximately 216.188 units.</p>

69 <p>Well explained 👍</p>

70 <h2>FAQ on Square Root of 3375</h2>

71 <h3>1.What is √3375 in its simplest form?</h3>

72 <p>The prime factorization of 3375 is 3^4 x 5^3, so the simplest form of √3375 is √(3^4 x 5^3).</p>

73 <h3>2.Mention the factors of 3375.</h3>

74 <p>Factors of 3375 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 675, 1125, and 3375.</p>

75 <h3>3.Calculate the square of 3375.</h3>

76 <p>We get the square of 3375 by multiplying the number by itself, that is 3375 x 3375 = 11390625.</p>

77 <h3>4.Is 3375 a prime number?</h3>

78 <p>3375 is not a<a>prime number</a>, as it has more than two factors.</p>

79 <h3>5.3375 is divisible by?</h3>

80 <p>3375 has many factors; those are 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 675, 1125, and 3375.</p>

81 <h2>Important Glossaries for the Square Root of 3375</h2>

82 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, so √16 = 4.</li>

83 </ul><ul><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>

84 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is often more relevant in practical applications, which is why it is also known as the principal square root.</li>

85 </ul><ul><li><strong>Prime factorization:</strong>Breaking down a number into its basic building blocks, specifically prime numbers. For example, the prime factorization of 3375 is 3^4 x 5^3.</li>

86 </ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of a non-perfect square by dividing the number into groups and using a systematic approach to approximate the square root.</li>

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

88 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

91 <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>

92 <h3>Fun Fact</h3>

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