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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 1225.</p>

4 <h2>What is the Square Root of 1225?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1225 is a<a>perfect square</a>. The square root of 1225 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1225, whereas (1225)^(1/2) in the<a>exponential form</a>. √1225 = 35, 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 1225</h2>

7 <p>The<a>prime factorization</a>method is typically used for perfect square numbers like 1225. The<a>long division</a>method and approximation method are more suited for non-perfect square numbers. Let us now learn the following method:</p>

8 <p>Prime factorization method</p>

9 <h2>Square Root of 1225 by Prime Factorization Method</h2>

10 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 1225 is broken down into its prime factors.</p>

11 <p><strong>Step 1:</strong>Finding the prime factors of 1225 Breaking it down, we get 5 x 5 x 7 x 7: 5^2 x 7^2 Step 2: Now we found out the prime factors of 1225. The second step is to make pairs of those prime factors. Since 1225 is a perfect square, the digits of the number can be grouped into pairs.</p>

12 <p>Therefore, calculating √1225 using prime factorization gives us 5 x 7 = 35.</p>

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15 <h2>Square Root of 1225 by Long Division Method</h2>

14 <h2>Square Root of 1225 by Long Division Method</h2>

16 <p>The long<a>division</a>method is generally used for non-perfect square numbers but can be demonstrated for perfect squares like 1225 for practice. In this method, we verify that our calculation matches the known perfect<a>square root</a>.</p>

15 <p>The long<a>division</a>method is generally used for non-perfect square numbers but can be demonstrated for perfect squares like 1225 for practice. In this method, we verify that our calculation matches the known perfect<a>square root</a>.</p>

17 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1225, we need to group it as 12 and 25.</p>

16 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1225, we need to group it as 12 and 25.</p>

18 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 12. We can say n is ‘3’ because 3 x 3 = 9 is less than 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, the<a>remainder</a>is 3.</p>

17 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 12. We can say n is ‘3’ because 3 x 3 = 9 is less than 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, the<a>remainder</a>is 3.</p>

19 <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, 3 + 3 = 6, which will be our new divisor.</p>

18 <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, 3 + 3 = 6, which will be our new divisor.</p>

20 <p><strong>Step 4:</strong>The next step is finding 6n x n ≤ 325. Let us consider n as 5; now 65 x 5 = 325.</p>

19 <p><strong>Step 4:</strong>The next step is finding 6n x n ≤ 325. Let us consider n as 5; now 65 x 5 = 325.</p>

21 <p><strong>Step 5:</strong>Subtract 325 from 325, and the remainder is 0. The quotient is 35.</p>

20 <p><strong>Step 5:</strong>Subtract 325 from 325, and the remainder is 0. The quotient is 35.</p>

22 <p><strong>Step 6:</strong>Since the remainder is 0, we can conclude that √1225 = 35.</p>

21 <p><strong>Step 6:</strong>Since the remainder is 0, we can conclude that √1225 = 35.</p>

23 <h2>Square Root of 1225 by Approximation Method</h2>

22 <h2>Square Root of 1225 by Approximation Method</h2>

24 <p>The approximation method is not necessary for 1225 as it is a perfect square, but it can be used to verify the calculation.</p>

23 <p>The approximation method is not necessary for 1225 as it is a perfect square, but it can be used to verify the calculation.</p>

25 <p><strong>Step 1:</strong>We find the closest perfect square to 1225, which are 1225 itself or nearby perfect squares.</p>

24 <p><strong>Step 1:</strong>We find the closest perfect square to 1225, which are 1225 itself or nearby perfect squares.</p>

26 <p><strong>Step 2:</strong>Since 1225 is a perfect square, √1225 directly gives us an integer value, which is 35.</p>

25 <p><strong>Step 2:</strong>Since 1225 is a perfect square, √1225 directly gives us an integer value, which is 35.</p>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1225</h2>

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1225</h2>

28 <p>Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping prime factorization steps. Let us look at a few common mistakes in detail.</p>

27 <p>Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping prime factorization steps. Let us look at a few common mistakes in detail.</p>

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29 <h3>Problem 1</h3>

30 <p>Can you help Max find the area of a square box if its side length is given as √1024?</p>

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

32 <p>The area of the square is 1024 square units.</p>

33 <h3>Explanation</h3>

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

35 <p>The side length is given as √1024.</p>

36 <p>Area of the square = side^2 = √1024 x √1024 = 32 × 32 = 1024.</p>

37 <p>Therefore, the area of the square box is 1024 square units.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

40 <p>A square-shaped building measuring 1225 square feet is built; if each of the sides is √1225, what will be the square feet of half of the building?</p>

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

42 <p>612.5 square feet</p>

43 <h3>Explanation</h3>

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

45 <p>Dividing 1225 by 2 = we get 612.5.</p>

46 <p>So half of the building measures 612.5 square feet.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate √1225 x 4.</p>

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

51 <p>140</p>

52 <h3>Explanation</h3>

53 <p>The first step is to find the square root of 1225, which is 35.</p>

54 <p>The second step is to multiply 35 by 4.</p>

55 <p>So 35 x 4 = 140.</p>

56 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

58 <p>What will be the square root of (625 + 600)?</p>

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

60 <p>The square root is 35.</p>

61 <h3>Explanation</h3>

62 <p>To find the square root, we need to find the sum of (625 + 600).</p>

63 <p>625 + 600 = 1225, and then √1225 = 35.</p>

64 <p>Therefore, the square root of (625 + 600) is ±35.</p>

65 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

67 <p>Find the perimeter of the rectangle if its length ‘l’ is √1225 units and the width ‘w’ is 50 units.</p>

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

69 <p>The perimeter of the rectangle is 170 units.</p>

70 <h3>Explanation</h3>

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

72 <p>Perimeter = 2 × (√1225 + 50)</p>

73 <p>= 2 × (35 + 50)</p>

74 <p>= 2 × 85</p>

75 <p>= 170 units.</p>

76 <p>Well explained 👍</p>

77 <h2>FAQ on Square Root of 1225</h2>

78 <h3>1.What is √1225 in its simplest form?</h3>

79 <p>The prime factorization of 1225 is 5 x 5 x 7 x 7, so the simplest form of √1225 = √(5 x 5 x 7 x 7) = 35.</p>

80 <h3>2.Mention the factors of 1225.</h3>

81 <p>Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, and 1225.</p>

82 <h3>3.Calculate the square of 35.</h3>

83 <p>We get the square of 35 by multiplying the number by itself, that is 35 x 35 = 1225.</p>

84 <h3>4.Is 1225 a prime number?</h3>

85 <p>1225 is not a<a>prime number</a>, as it has more than two factors.</p>

86 <h3>5.1225 is divisible by?</h3>

87 <p>1225 has several factors; those are 1, 5, 7, 25, 35, 49, 175, 245, and 1225.</p>

88 <h2>Important Glossaries for the Square Root of 1225</h2>

89 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, that is √36 = 6. </li>

90 <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>

91 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example: 36, 49, 64, etc. </li>

92 <li><strong>Prime factorization:</strong>Prime factorization is expressing a number as the product of its prime numbers. </li>

93 <li><strong>Integer:</strong>An integer is a whole number that can be positive, negative, or zero. Examples include -5, -4, 0, 1, 2, etc.</li>

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

95 <p>▶</p>

96 <h2>Jaskaran Singh Saluja</h2>

97 <h3>About the Author</h3>

98 <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>

99 <h3>Fun Fact</h3>

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