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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 1348.</p>

4 <h2>What is the Square Root of 1348?</h2>

5 <p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 1348 is not a<a>perfect square</a>. The square root of 1348 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1348, whereas (1348)^(1/2) in the exponential form. √1348 ≈ 36.719, 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 1348</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 1348 by Prime Factorization Method</h2>

12 <p>The prime factorization of a number is its<a>expression</a>as a<a>product</a>of prime<a>factors</a>. Now let us look at how 1348 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1348</p>

14 <p>Breaking it down, we get 2 x 2 x 337: 2^2 x 337^1</p>

15 <p><strong>Step 2:</strong>Now that we have found the prime factors of 1348, we attempt to make pairs of those prime factors. Since 1348 is not a perfect square, calculating √1348 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 1348 by Long Division Method</h2>

17 <h2>Square Root of 1348 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>Start by grouping the digits of 1348 from right to left in pairs. We have 13 and 48.</p>

19 <p><strong>Step 1:</strong>Start by grouping the digits of 1348 from right to left in pairs. We have 13 and 48.</p>

21 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 13. This number is 3, since 3 x 3 = 9.</p>

20 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 13. This number is 3, since 3 x 3 = 9.</p>

22 <p><strong>Step 3:</strong>Subtract 9 from 13 to get 4. Bring down the next pair, 48, to have 448.</p>

21 <p><strong>Step 3:</strong>Subtract 9 from 13 to get 4. Bring down the next pair, 48, to have 448.</p>

23 <p><strong>Step 4:</strong>Double the<a>divisor</a>(3) to get 6, and<a>set</a>up a new divisor as 6n, where n is a digit that, when placed next to 6, forms a number that fits into 448.</p>

22 <p><strong>Step 4:</strong>Double the<a>divisor</a>(3) to get 6, and<a>set</a>up a new divisor as 6n, where n is a digit that, when placed next to 6, forms a number that fits into 448.</p>

24 <p><strong>Step 5:</strong>Determine n such that 6n x n is less than or equal to 448. Let n be 7, as 67 x 7 = 469 is too large, and 66 x 6 = 396 fits.</p>

23 <p><strong>Step 5:</strong>Determine n such that 6n x n is less than or equal to 448. Let n be 7, as 67 x 7 = 469 is too large, and 66 x 6 = 396 fits.</p>

25 <p><strong>Step 6:</strong>Subtract 396 from 448 to get 52.</p>

24 <p><strong>Step 6:</strong>Subtract 396 from 448 to get 52.</p>

26 <p><strong>Step 7:</strong>Bring down two zeros to make it 5200, and repeat the process to get more<a>decimal</a>places.</p>

25 <p><strong>Step 7:</strong>Bring down two zeros to make it 5200, and repeat the process to get more<a>decimal</a>places.</p>

27 <p><strong>Step 8:</strong>Continue the process to get a more precise value, yielding approximately √1348 ≈ 36.719.</p>

26 <p><strong>Step 8:</strong>Continue the process to get a more precise value, yielding approximately √1348 ≈ 36.719.</p>

28 <h2>Square Root of 1348 by Approximation Method</h2>

27 <h2>Square Root of 1348 by Approximation Method</h2>

29 <p>The approximation method is another method for finding the 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 1348 using the approximation method:</p>

28 <p>The approximation method is another method for finding the 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 1348 using the approximation method:</p>

30 <p><strong>Step 1:</strong>Identify the closest perfect squares around 1348. The smallest perfect square less than 1348 is 1296 (36^2) and the largest perfect square<a>greater than</a>1348 is 1369 (37^2).</p>

29 <p><strong>Step 1:</strong>Identify the closest perfect squares around 1348. The smallest perfect square less than 1348 is 1296 (36^2) and the largest perfect square<a>greater than</a>1348 is 1369 (37^2).</p>

31 <p><strong>Step 2:</strong>Since √1348 is between 36 and 37, we can use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square)</p>

30 <p><strong>Step 2:</strong>Since √1348 is between 36 and 37, we can use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square)</p>

32 <p><strong>Step 3:</strong>Apply the formula: (1348 - 1296) / (1369 - 1296) = 52 / 73 ≈ 0.712 Step 4: Add this decimal to the smaller square root: 36 + 0.712 = 36.712. So √1348 ≈ 36.719.</p>

31 <p><strong>Step 3:</strong>Apply the formula: (1348 - 1296) / (1369 - 1296) = 52 / 73 ≈ 0.712 Step 4: Add this decimal to the smaller square root: 36 + 0.712 = 36.712. So √1348 ≈ 36.719.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1348</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1348</h2>

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

33 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these 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 √1348?</p>

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

38 <p>The area of the square is 1348 square units.</p>

39 <h3>Explanation</h3>

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

41 <p>The side length is given as √1348.</p>

42 <p>Area of the square = side^2 = √1348 x √1348 = 1348.</p>

43 <p>Therefore, the area of the square box is 1348 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped piece of land measuring 1348 square feet is being developed; if each of the sides is √1348, what will be the square feet of half of the land?</p>

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

48 <p>674 square feet</p>

49 <h3>Explanation</h3>

50 <p>We can simply divide the given area by 2 since the land is square-shaped.</p>

51 <p>Dividing 1348 by 2 gives us 674.</p>

52 <p>So half of the land measures 674 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √1348 x 5.</p>

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

57 <p>183.595</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 1348, which is approximately 36.719.</p>

60 <p>The second step is to multiply 36.719 by 5.</p>

61 <p>So 36.719 x 5 = 183.595.</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

64 <p>What will be the square root of (1348 + 21)?</p>

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

66 <p>The square root is approximately 37.</p>

67 <h3>Explanation</h3>

68 <p>To find the square root, first find the sum of (1348 + 21). 1348 + 21 = 1369, and √1369 = 37.</p>

69 <p>Therefore, the square root of (1348 + 21) is ±37.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √1348 units and the width ‘w’ is 40 units.</p>

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

74 <p>The perimeter of the rectangle is approximately 153.438 units.</p>

75 <h3>Explanation</h3>

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

77 <p>Perimeter = 2 × (√1348 + 40) = 2 × (36.719 + 40) = 2 × 76.719 = 153.438 units.</p>

78 <p>Well explained 👍</p>

79 <h2>FAQ on Square Root of 1348</h2>

80 <h3>1.What is √1348 in its simplest form?</h3>

81 <p>The prime factorization of 1348 is 2 x 2 x 337, so the simplest form of √1348 is √(2^2 x 337).</p>

82 <h3>2.Mention the factors of 1348.</h3>

83 <p>Factors of 1348 are 1, 2, 4, 337, 674, and 1348.</p>

84 <h3>3.Calculate the square of 1348.</h3>

85 <p>We get the square of 1348 by multiplying the number by itself, which is 1348 x 1348 = 1,818,304.</p>

86 <h3>4.Is 1348 a prime number?</h3>

87 <p>1348 is not a<a>prime number</a>, as it has more than two factors.</p>

88 <h3>5.1348 is divisible by?</h3>

89 <p>1348 has several factors; those are 1, 2, 4, 337, 674, and 1348.</p>

90 <h2>Important Glossaries for the Square Root of 1348</h2>

91 <ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 4^2 = 16, and the square root of 16 is √16 = 4.</li>

92 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written as a simple fraction - it has a non-repeating, non-terminating decimal expansion.</li>

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

94 </ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of a number by dividing and averaging, typically used for non-perfect squares.</li>

95 </ul><ul><li><strong>Radical notation:</strong>The expression of a square root using the radical sign (√). For example, √25 = 5.</li>

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

97 <p>▶</p>

98 <h2>Jaskaran Singh Saluja</h2>

99 <h3>About the Author</h3>

100 <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>

101 <h3>Fun Fact</h3>

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