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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 vehicle design, finance, etc. Here, we will discuss the square root of 5625.</p>

4 <h2>What is the Square Root of 5625?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 5625 is a<a>perfect square</a>. The square root of 5625 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √5625, whereas (5625)^(1/2) in the exponential form. √5625 = 75, 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 5625</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. The prime factorization method is effective for finding the<a>square root</a>of perfect squares like 5625. 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 5625 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 5625 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 5625 Breaking it down, we get 3 x 3 x 5 x 5 x 5 x 5: 3^2 x 5^4</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 5625. The second step is to make pairs of those prime factors. Since 5625 is a perfect square, we can group the digits into pairs.</p>

15 <p>Thus, √5625 = 3 x 5 x 5 = 75.</p>

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18 <h2>Square Root of 5625 by Long Division Method</h2>

17 <h2>Square Root of 5625 by Long Division Method</h2>

19 <p>The<a>long division</a>method can be used for both perfect and 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 square root using the long division method, step by step.</p>

18 <p>The<a>long division</a>method can be used for both perfect and 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 square root 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 5625, we need to group it as 56 and 25.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 5625, we need to group it as 56 and 25.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 56. We can say n as ‘7’ because 7 x 7 = 49, which is<a>less than</a>or equal to 56. Now the<a>quotient</a>is 7. After subtracting 56 - 49, the<a>remainder</a>is 7.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 56. We can say n as ‘7’ because 7 x 7 = 49, which is<a>less than</a>or equal to 56. Now the<a>quotient</a>is 7. After subtracting 56 - 49, the<a>remainder</a>is 7.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 25, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 7 + 7, we get 14, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 25, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 7 + 7, we get 14, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 14n as the new divisor, we need to find the value of n.</p>

22 <p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 14n as the new divisor, we need to find the value of n.</p>

24 <p><strong>Step 5:</strong>The next step is finding 14n × n ≤ 725. Let us consider n as 5, now 145 x 5 = 725.</p>

23 <p><strong>Step 5:</strong>The next step is finding 14n × n ≤ 725. Let us consider n as 5, now 145 x 5 = 725.</p>

25 <p><strong>Step 6:</strong>Subtract 725 from 725, the difference is 0, and the quotient is 75.</p>

24 <p><strong>Step 6:</strong>Subtract 725 from 725, the difference is 0, and the quotient is 75.</p>

26 <p>So, the square root of √5625 is 75.</p>

25 <p>So, the square root of √5625 is 75.</p>

27 <h2>Square Root of 5625 by Approximation Method</h2>

26 <h2>Square Root of 5625 by Approximation Method</h2>

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 5625 using the approximation method.</p>

27 <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 5625 using the approximation method.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √5625.</p>

28 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √5625.</p>

30 <p>The smallest perfect square of 5625 is 5476 and the largest perfect square is 5776. √5625 falls exactly at 75.</p>

29 <p>The smallest perfect square of 5625 is 5476 and the largest perfect square is 5776. √5625 falls exactly at 75.</p>

31 <p><strong>Step 2:</strong>Since 5625 is a perfect square, we can directly find the square root.</p>

30 <p><strong>Step 2:</strong>Since 5625 is a perfect square, we can directly find the square root.</p>

32 <p>Therefore, the square root of 5625 is 75.</p>

31 <p>Therefore, the square root of 5625 is 75.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5625</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5625</h2>

34 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

33 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

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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 √625?</p>

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

38 <p>The area of the square is 625 square units.</p>

39 <h3>Explanation</h3>

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

41 <p>The side length is given as √625.</p>

42 <p>Area of the square = side² = √625 x √625 = 25 × 25 = 625.</p>

43 <p>Therefore, the area of the square box is 625 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped building measuring 5625 square feet is built; if each of the sides is √5625, what will be the square feet of half of the building?</p>

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

48 <p>2812.5 square feet</p>

49 <h3>Explanation</h3>

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

51 <p>Dividing 5625 by 2 = we get 2812.5.</p>

52 <p>So, half of the building measures 2812.5 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √5625 x 4.</p>

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

57 <p>300</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 5625, which is 75.</p>

60 <p>The second step is to multiply 75 with 4.</p>

61 <p>So, 75 x 4 = 300.</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

64 <p>What will be the square root of (5625 + 375)?</p>

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

66 <p>The square root is 80.</p>

67 <h3>Explanation</h3>

68 <p>To find the square root, we need to find the sum of (5625 + 375). 5625 + 375 = 6000, and then √6000 ≈ 77.46.</p>

69 <p>Therefore, the square root of (5625 + 375) is approximately ±77.46.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √400 units and the width ‘w’ is 25 units.</p>

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

74 <p>We find the perimeter of the rectangle as 90 units.</p>

75 <h3>Explanation</h3>

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

77 <p>Perimeter = 2 × (√400 + 25) = 2 × (20 + 25) = 2 × 45 = 90 units.</p>

78 <p>Well explained 👍</p>

79 <h2>FAQ on Square Root of 5625</h2>

80 <h3>1.What is √5625 in its simplest form?</h3>

81 <p>The prime factorization of 5625 is 3 x 3 x 5 x 5 x 5 x 5, so the simplest form of √5625 = 3 x 5 x 5 = 75.</p>

82 <h3>2.Mention the factors of 5625.</h3>

83 <p>Factors of 5625 are 1, 3, 5, 15, 25, 75, 225, 1125, 1875, and 5625.</p>

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

85 <p>We get the square of 75 by multiplying the number by itself, that is 75 x 75 = 5625.</p>

86 <h3>4.Is 5625 a prime number?</h3>

87 <p>5625 is not a<a>prime number</a>, as it has more than two factors.</p>

88 <h3>5.5625 is divisible by?</h3>

89 <p>5625 has many factors; some of those are 1, 3, 5, 15, 25, 75, 225, 1125, 1875, and 5625.</p>

90 <h2>Important Glossaries for the Square Root of 5625</h2>

91 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root that is √81 = 9.</li>

92 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>

93 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 64 is a perfect square because it is 8^2.</li>

94 </ul><ul><li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of its prime factors. For instance, the prime factorization of 36 is 2^2 x 3^2.</li>

95 </ul><ul><li><strong>Long division method:</strong>The long division method is a technique used to find the square root of both perfect and non-perfect squares through step-by-step division.</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>