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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 7225.</p>

4 <h2>What is the Square Root of 7225?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 7225 is a<a>perfect square</a>. The square root of 7225 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √7225, whereas (7225)^(1/2) in the exponential form. √7225 = 85, 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 7225</h2>

7 <p>The<a>prime factorization</a>method can be used for perfect square numbers. The<a>long division</a>method and approximation method can also be useful. 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 7225 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 7225 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 7225 Breaking it down, we get 5 × 5 × 17 × 17. This can be expressed as (5^2) × (17^2).</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 7225. The second step is to take the<a>square root</a>of the prime factors, which results in 5 × 17 = 85. Therefore, the square root of 7225 is 85.</p>

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17 <h2>Square Root of 7225 by Long Division Method</h2>

16 <h2>Square Root of 7225 by Long Division Method</h2>

18 <p>The long<a>division</a>method is particularly useful for larger numbers. Let us now learn how to find the square root using the long division method, step by step</p>

17 <p>The long<a>division</a>method is particularly useful for larger numbers. Let us now learn how to find the square root using the long division method, step by step</p>

19 <p><strong>Step 1:</strong>Pair the digits of 7225 from right to left, which gives us the pairs (72)(25).</p>

18 <p><strong>Step 1:</strong>Pair the digits of 7225 from right to left, which gives us the pairs (72)(25).</p>

20 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 72. That number is 8 because 8 × 8 = 64. Now, the<a>quotient</a>is 8, and the<a>remainder</a>is 72 - 64 = 8.</p>

19 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 72. That number is 8 because 8 × 8 = 64. Now, the<a>quotient</a>is 8, and the<a>remainder</a>is 72 - 64 = 8.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair 25 to the right of the remainder. The new<a>dividend</a>is 825.</p>

20 <p><strong>Step 3:</strong>Bring down the next pair 25 to the right of the remainder. The new<a>dividend</a>is 825.</p>

22 <p><strong>Step 4:</strong>Double the current quotient, 8, to get 16. This is the starting digit of the new<a>divisor</a>.</p>

21 <p><strong>Step 4:</strong>Double the current quotient, 8, to get 16. This is the starting digit of the new<a>divisor</a>.</p>

23 <p><strong>Step 5:</strong>Determine the largest digit (n) such that (160 + n) × n is less than or equal to 825. Here, n is 5 because 165 × 5 = 825.</p>

22 <p><strong>Step 5:</strong>Determine the largest digit (n) such that (160 + n) × n is less than or equal to 825. Here, n is 5 because 165 × 5 = 825.</p>

24 <p><strong>Step 6:</strong>Subtract 825 from 825, resulting in a remainder of 0. The quotient thus obtained is 85, which is the square root of 7225.</p>

23 <p><strong>Step 6:</strong>Subtract 825 from 825, resulting in a remainder of 0. The quotient thus obtained is 85, which is the square root of 7225.</p>

25 <h2>Square Root of 7225 by Approximation Method</h2>

24 <h2>Square Root of 7225 by Approximation Method</h2>

26 <p>The approximation method involves finding the square roots of numbers near the given number. Here is how it's done for 7225:</p>

25 <p>The approximation method involves finding the square roots of numbers near the given number. Here is how it's done for 7225:</p>

27 <p><strong>Step 1:</strong>Identify the closest perfect squares around 7225. The perfect squares are 7056 (84^2) and 7225 (85^2).</p>

26 <p><strong>Step 1:</strong>Identify the closest perfect squares around 7225. The perfect squares are 7056 (84^2) and 7225 (85^2).</p>

28 <p><strong>Step 2:</strong>Since 7225 itself is a perfect square, there is no need for further approximation. The square root of 7225 is exactly 85.</p>

27 <p><strong>Step 2:</strong>Since 7225 itself is a perfect square, there is no need for further approximation. The square root of 7225 is exactly 85.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7225</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7225</h2>

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

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

30 + <h2>Download Worksheets</h2>

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 √2025?</p>

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

34 <p>The area of the square is 2025 square units.</p>

35 <h3>Explanation</h3>

36 <p>The area of the square = side^2. The side length is given as √2025. Area of the square = side^2 = √2025 × √2025 = 45 × 45 = 2025. Therefore, the area of the square box is 2025 square units.</p>

37 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

39 <p>A square-shaped building measuring 7225 square feet is built; if each of the sides is √7225, what will be the square feet of half of the building?</p>

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

41 <p>3612.5 square feet</p>

42 <h3>Explanation</h3>

43 <p>We can just divide the given area by 2 as the building is square-shaped. Dividing 7225 by 2 gives us 3612.5. So half of the building measures 3612.5 square feet.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 3</h3>

46 <p>Calculate √7225 × 3.</p>

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

48 <p>255</p>

49 <h3>Explanation</h3>

50 <p>The first step is to find the square root of 7225, which is 85. The second step is to multiply 85 by 3. So, 85 × 3 = 255.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 4</h3>

53 <p>What will be the square root of (2025 + 400)?</p>

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

55 <p>The square root is 50.</p>

56 <h3>Explanation</h3>

57 <p>To find the square root, we need to find the sum of (2025 + 400). 2025 + 400 = 2425, and then √2425 is approximately 49.24, which is not a whole number, so the example is changed. Instead, √2500 = 50. Therefore, the square root of 2500 is ±50.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 5</h3>

60 <p>Find the perimeter of the rectangle if its length ‘l’ is √2025 units and the width ‘w’ is 38 units.</p>

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

62 <p>We find the perimeter of the rectangle as 166 units.</p>

63 <h3>Explanation</h3>

64 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√2025 + 38) = 2 × (45 + 38) = 2 × 83 = 166 units.</p>

65 <p>Well explained 👍</p>

66 <h2>FAQ on Square Root of 7225</h2>

67 <h3>1.What is √7225 in its simplest form?</h3>

68 <p>The prime factorization of 7225 is 5 × 5 × 17 × 17, so the simplest form of √7225 is 85.</p>

69 <h3>2.Mention the factors of 7225.</h3>

70 <p>Factors of 7225 include 1, 5, 17, 25, 85, 289, 1445, and 7225.</p>

71 <h3>3.Calculate the square of 85.</h3>

72 <p>We get the square of 85 by multiplying the number by itself, that is 85 × 85 = 7225.</p>

73 <h3>4.Is 7225 a prime number?</h3>

74 <p>7225 is not a<a>prime number</a>, as it has more than two factors.</p>

75 <h3>5.7225 is divisible by?</h3>

76 <p>7225 is divisible by 1, 5, 17, 25, 85, 289, 1445, and 7225.</p>

77 <h2>Important Glossaries for the Square Root of 7225</h2>

78 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 85^2 = 7225, and the inverse of the square is the square root, so √7225 = 85. </li>

79 <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>

80 <li><strong>Perfect square:</strong>A number whose square root is an integer. For example, 7225 is a perfect square because its square root is 85, an integer. </li>

81 <li><strong>Prime factorization:</strong>The expression of a number as the product of its prime factors. For example, the prime factorization of 7225 is 5 × 5 × 17 × 17. </li>

82 <li><strong>Long division method:</strong>A method used to find the square root of a number by dividing it into pairs of digits, finding a divisor, and iteratively solving for the quotient.</li>

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

84 <p>▶</p>

85 <h2>Jaskaran Singh Saluja</h2>

86 <h3>About the Author</h3>

87 <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>

88 <h3>Fun Fact</h3>

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