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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 448.</p>

4 <h2>What is the Square Root of 448?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 448 is not a<a>perfect square</a>. The square root of 448 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √448, whereas (448)^(1/2) in the exponential form. √448 ≈ 21.166, 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 448</h2>

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

8 <ul><li>Prime factorization method </li>

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

10 </ul><ul><li>Approximation method</li>

11 </ul><h2>Square Root of 448 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 448 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 448. Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 7:<a>2^5</a>x 7.</p>

14 <p><strong>Step 2:</strong>Now we found the prime factors of 448. The second step is to make pairs of those prime factors. Since 448 is not a perfect square, the digits of the number can’t be grouped into complete pairs.</p>

15 <p>Therefore, calculating 448 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 448 by Long Division Method</h2>

17 <h2>Square Root of 448 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>To begin with, we need to group the numbers from right to left. In the case of 448, we need to group it as 48 and 4.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 448, we need to group it as 48 and 4.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n is ‘2’ because 2 x 2 is equal to 4. Now the<a>quotient</a>is 2 after subtracting 4 from 4, the<a>remainder</a>is 0.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n is ‘2’ because 2 x 2 is equal to 4. Now the<a>quotient</a>is 2 after subtracting 4 from 4, the<a>remainder</a>is 0.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 48, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 2 + 2, to get 4, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 48, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 2 + 2, to get 4, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor will be part of finding 4n ≤ 48. Let us consider n as 1, now 4 x 1 = 4.</p>

22 <p><strong>Step 4:</strong>The new divisor will be part of finding 4n ≤ 48. Let us consider n as 1, now 4 x 1 = 4.</p>

24 <p><strong>Step 5:</strong>Subtract 48 from 4; the difference is 44, and the quotient is 21.</p>

23 <p><strong>Step 5:</strong>Subtract 48 from 4; the difference is 44, and the quotient is 21.</p>

25 <p><strong>Step 6:</strong>Since the dividend is<a>less than</a>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 4400.</p>

24 <p><strong>Step 6:</strong>Since the dividend is<a>less than</a>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 4400.</p>

26 <p><strong>Step 7:</strong>Now we need to find a new divisor that is 42 because 421 ✖ 9 = 3789.</p>

25 <p><strong>Step 7:</strong>Now we need to find a new divisor that is 42 because 421 ✖ 9 = 3789.</p>

27 <p><strong>Step 8:</strong>Subtracting 3789 from 4400, we get the result 611.</p>

26 <p><strong>Step 8:</strong>Subtracting 3789 from 4400, we get the result 611.</p>

28 <p><strong>Step 9:</strong>Now the quotient is 21.1.</p>

27 <p><strong>Step 9:</strong>Now the quotient is 21.1.</p>

29 <p><strong>Step 10:</strong>Continue these steps until we get a precise enough value.</p>

28 <p><strong>Step 10:</strong>Continue these steps until we get a precise enough value.</p>

30 <p>So the square root of √448 ≈ 21.166.</p>

29 <p>So the square root of √448 ≈ 21.166.</p>

31 <h2>Square Root of 448 by Approximation Method</h2>

30 <h2>Square Root of 448 by Approximation Method</h2>

32 <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 448 using the approximation method.</p>

31 <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 448 using the approximation method.</p>

33 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √448. The smallest perfect square less than 448 is 441, and the largest perfect square<a>greater than</a>448 is 484. √448 falls somewhere between 21 and 22.</p>

32 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √448. The smallest perfect square less than 448 is 441, and the largest perfect square<a>greater than</a>448 is 484. √448 falls somewhere between 21 and 22.</p>

34 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>

33 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>

35 <p>Going by the formula (448 - 441) ÷ (484 - 441) = 0.16.</p>

34 <p>Going by the formula (448 - 441) ÷ (484 - 441) = 0.16.</p>

36 <p>Using the formula, we identified the<a>decimal</a>value.</p>

35 <p>Using the formula, we identified the<a>decimal</a>value.</p>

37 <p>The next step is adding the value we got initially to the decimal number, which is 21 + 0.16 = 21.16, so the square root of 448 is approximately 21.16.</p>

36 <p>The next step is adding the value we got initially to the decimal number, which is 21 + 0.16 = 21.16, so the square root of 448 is approximately 21.16.</p>

38 <h2>Common Mistakes and How to Avoid Them in the Square Root of 448</h2>

37 <h2>Common Mistakes and How to Avoid Them in the Square Root of 448</h2>

39 <p>Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.</p>

38 <p>Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.</p>

39 + <h2>Download Worksheets</h2>

40 <h3>Problem 1</h3>

41 <p>Can you help Max find the area of a square box if its side length is given as √448?</p>

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

43 <p>The area of the square is approximately 448 square units.</p>

44 <h3>Explanation</h3>

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

46 <p>The side length is given as √448.</p>

47 <p>Area of the square = side² = √448 x √448 = 448.</p>

48 <p>Therefore, the area of the square box is 448 square units.</p>

49 <p>Well explained 👍</p>

50 <h3>Problem 2</h3>

51 <p>A square-shaped building measuring 448 square feet is built; if each of the sides is √448, what will be the square feet of half of the building?</p>

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

53 <p>224 square feet.</p>

54 <h3>Explanation</h3>

55 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

56 <p>Dividing 448 by 2 gives us 224.</p>

57 <p>So half of the building measures 224 square feet.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 3</h3>

60 <p>Calculate √448 x 5.</p>

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

62 <p>Approximately 105.83.</p>

63 <h3>Explanation</h3>

64 <p>The first step is to find the square root of 448, which is approximately 21.166, and then multiply 21.166 by 5.</p>

65 <p>So 21.166 x 5 ≈ 105.83.</p>

66 <p>Well explained 👍</p>

67 <h3>Problem 4</h3>

68 <p>What will be the square root of (441 + 7)?</p>

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

70 <p>The square root is approximately 21.33.</p>

71 <h3>Explanation</h3>

72 <p>To find the square root, we need to find the sum of (441 + 7). 441 + 7 = 448, and then √448 ≈ 21.166.</p>

73 <p>Therefore, the square root of (441 + 7) is approximately 21.166.</p>

74 <p>Well explained 👍</p>

75 <h3>Problem 5</h3>

76 <p>Find the perimeter of the rectangle if its length ‘l’ is √448 units and the width ‘w’ is 38 units.</p>

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

78 <p>We find the perimeter of the rectangle as approximately 118.33 units.</p>

79 <h3>Explanation</h3>

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

81 <p>Perimeter = 2 × (√448 + 38) ≈ 2 × (21.166 + 38) = 2 × 59.166 ≈ 118.33 units.</p>

82 <p>Well explained 👍</p>

83 <h2>FAQ on Square Root of 448</h2>

84 <h3>1.What is √448 in its simplest form?</h3>

85 <p>The prime factorization of 448 is 2 x 2 x 2 x 2 x 2 x 7, so the simplest form of √448 = √(2^5 x 7).</p>

86 <h3>2.Mention the factors of 448.</h3>

87 <p>Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448.</p>

88 <h3>3.Calculate the square of 448.</h3>

89 <p>We get the square of 448 by multiplying the number by itself, that is 448 x 448 = 200704.</p>

90 <h3>4.Is 448 a prime number?</h3>

91 <h3>5.448 is divisible by?</h3>

92 <p>448 has many factors; those are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448.</p>

93 <h2>Important Glossaries for the Square Root of 448</h2>

94 <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, that is √16 = 4.</li>

95 </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>

96 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is used more often due to its applications in the real world. This is known as the principal square root.</li>

97 </ul><ul><li><strong>Prime factorization:</strong>The process of breaking down a number into its prime factors. For example, the prime factorization of 448 is 2^5 x 7.</li>

98 </ul><ul><li><strong>Approximation method:</strong>A technique used to estimate the square root of a non-perfect square by identifying its closest perfect squares.</li>

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

100 <p>▶</p>

101 <h2>Jaskaran Singh Saluja</h2>

102 <h3>About the Author</h3>

103 <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>

104 <h3>Fun Fact</h3>

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