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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 such as vehicle design and finance. Here, we will discuss the square root of 2401.</p>

4 <h2>What is the Square Root of 2401?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 2401 is a<a>perfect square</a>. The square root of 2401 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √2401, whereas in exponential form it is expressed as (2401)^(1/2). √2401 = 49, which is a<a>rational number</a>because it can 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 2401</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. Since 2401 is a perfect square, we can use its prime factorization to find the<a>square root</a>. Let us now learn the following methods:</p>

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

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

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 2401 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 2401 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 2401 Breaking it down, we get 7 x 7 x 7 x 7; that is, 7^4.</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 2401. Since 2401 is a perfect square, the square root is the product of one number from each pair of the same factors.</p>

15 <p>Therefore, √2401 = 7 * 7 = 49.</p>

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18 <h2>Square Root of 2401 by Long Division Method</h2>

17 <h2>Square Root of 2401 by Long Division Method</h2>

19 <p>The<a>long division</a>method can also be used for perfect squares to verify the result. Let us now learn how to find the square root using the long division method, step by step.</p>

18 <p>The<a>long division</a>method can also be used for perfect squares to verify the result. Let us now learn how to find the square root using the long division method, step by step.</p>

20 <p><strong>Step 1:</strong>Group the numbers from right to left. In the case of 2401, group it as 24 and 01.</p>

19 <p><strong>Step 1:</strong>Group the numbers from right to left. In the case of 2401, group it as 24 and 01.</p>

21 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 24. Here, it is 4, as 4^2 = 16. Subtract 16 from 24 to get a<a>remainder</a>of 8.</p>

20 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 24. Here, it is 4, as 4^2 = 16. Subtract 16 from 24 to get a<a>remainder</a>of 8.</p>

22 <p><strong>Step 3:</strong>Bring down the next pair of digits, 01, to make the new<a>dividend</a>801.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair of digits, 01, to make the new<a>dividend</a>801.</p>

23 <p><strong>Step 4:</strong>Double the<a>divisor</a>(4) to get 8, and use it to find the next digit of the<a>quotient</a>. Find a digit x such that 8x * x is less than or equal to 801. Here, x is 9, as 89 * 9 = 801.</p>

22 <p><strong>Step 4:</strong>Double the<a>divisor</a>(4) to get 8, and use it to find the next digit of the<a>quotient</a>. Find a digit x such that 8x * x is less than or equal to 801. Here, x is 9, as 89 * 9 = 801.</p>

24 <p><strong>Step 5:</strong>Therefore, the quotient is 49, which is the square root of 2401.</p>

23 <p><strong>Step 5:</strong>Therefore, the quotient is 49, which is the square root of 2401.</p>

25 <h2>Square Root of 2401 by Approximation Method</h2>

24 <h2>Square Root of 2401 by Approximation Method</h2>

26 <p>The approximation method is generally used for finding the square roots of non-perfect squares. However, since 2401 is a perfect square, the exact root can be found without approximation. For completeness, we check the perfect squares near 2401:</p>

25 <p>The approximation method is generally used for finding the square roots of non-perfect squares. However, since 2401 is a perfect square, the exact root can be found without approximation. For completeness, we check the perfect squares near 2401:</p>

27 <p><strong>Step 1:</strong>The perfect squares closest to 2401 are 2304 (48^2) and 2500 (50^2). Since 2401 is a perfect square, its root is exactly 49, as it lies directly between these two numbers.</p>

26 <p><strong>Step 1:</strong>The perfect squares closest to 2401 are 2304 (48^2) and 2500 (50^2). Since 2401 is a perfect square, its root is exactly 49, as it lies directly between these two numbers.</p>

28 <p><strong>Step 2:</strong>No further approximation is necessary, as 2401 is a perfect square.</p>

27 <p><strong>Step 2:</strong>No further approximation is necessary, as 2401 is a perfect square.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 2401</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 2401</h2>

30 <p>Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

29 <p>Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

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31 <h3>Problem 1</h3>

32 <p>Can you help Max find the area of a square box if its side length is given as √2401?</p>

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

34 <p>The area of the square is 2401 square units.</p>

35 <h3>Explanation</h3>

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

37 <p>The side length is given as √2401.</p>

38 <p>Area of the square = side^2 = √2401 x √2401 = 49 × 49 = 2401.</p>

39 <p>Therefore, the area of the square box is 2401 square units.</p>

40 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

42 <p>A square-shaped building measuring 2401 square feet is built; if each of the sides is √2401, what will be the square feet of half of the building?</p>

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

44 <p>1200.5 square feet</p>

45 <h3>Explanation</h3>

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

47 <p>Dividing 2401 by 2 = we get 1200.5.</p>

48 <p>So half of the building measures 1200.5 square feet.</p>

49 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

51 <p>Calculate √2401 x 5.</p>

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

53 <p>245</p>

54 <h3>Explanation</h3>

55 <p>The first step is to find the square root of 2401, which is 49.</p>

56 <p>The second step is to multiply 49 by 5.</p>

57 <p>So 49 x 5 = 245.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

60 <p>What will be the square root of (2400 + 1)?</p>

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

62 <p>The square root is 49.</p>

63 <h3>Explanation</h3>

64 <p>To find the square root, we need to find the sum of (2400 + 1).</p>

65 <p>2400 + 1 = 2401, and then √2401 = 49.</p>

66 <p>Therefore, the square root of (2400 + 1) is ±49.</p>

67 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

69 <p>Find the perimeter of the rectangle if its length ‘l’ is √2401 units and the width ‘w’ is 38 units.</p>

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

71 <p>We find the perimeter of the rectangle as 174 units.</p>

72 <h3>Explanation</h3>

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

74 <p>Perimeter = 2 × (√2401 + 38) = 2 × (49 + 38) = 2 × 87 = 174 units.</p>

75 <p>Well explained 👍</p>

76 <h2>FAQ on Square Root of 2401</h2>

77 <h3>1.What is √2401 in its simplest form?</h3>

78 <p>The prime factorization of 2401 is 7 x 7 x 7 x 7, so the simplest form of √2401 = √(7 x 7 x 7 x 7) = 49.</p>

79 <h3>2.Mention the factors of 2401.</h3>

80 <p>Factors of 2401 are 1, 7, 49, 343, and 2401.</p>

81 <h3>3.Calculate the square of 49.</h3>

82 <p>We get the square of 49 by multiplying the number by itself, that is 49 x 49 = 2401.</p>

83 <h3>4.Is 2401 a prime number?</h3>

84 <p>2401 is not a<a>prime number</a>, as it has more than two factors.</p>

85 <h3>5.2401 is divisible by?</h3>

86 <p>2401 is divisible by 1, 7, 49, 343, and 2401.</p>

87 <h2>Important Glossaries for the Square Root of 2401</h2>

88 <ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, if 49^2 = 2401, then the square root of 2401 is 49.</li>

89 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.</li>

90 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 49 is a perfect square because it is 7^2.</li>

91 </ul><ul><li><strong>Prime factorization:</strong>Prime factorization is expressing a number as the product of its prime numbers. For instance, 2401 = 7^4.</li>

92 </ul><ul><li><strong>Long division method:</strong>A method used to find the square root of numbers by dividing and finding approximations step by step.</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>