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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 10625.</p>

4 <h2>What is the Square Root of 10625?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 10625 is a<a>perfect square</a>. The square root of 10625 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √10625, whereas (10625)^(1/2) in the exponential form. √10625 = 103, 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 10625</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. Let us now learn the following methods:</p>

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

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

10 </ul><h2>Square Root of 10625 by Prime Factorization Method</h2>

11 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 10625 is broken down into its prime factors.</p>

12 <p><strong>Step 1:</strong>Finding the prime factors of 10625</p>

13 <p>Breaking it down, we get 5 x 5 x 5 x 5 x 17: 5^4 x 17^1</p>

14 <p><strong>Step 2:</strong>Now that we found out the prime factors of 10625, the second step is to make pairs of those prime factors. Since 10625 is a perfect square, prime factors can be paired: (5 x 5), (5 x 5). Therefore, calculating 10625 using prime factorization gives us 103.</p>

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17 <h2>Square Root of 10625 by Long Division Method</h2>

16 <h2>Square Root of 10625 by Long Division Method</h2>

18 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

17 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 10625, we group it as 25 and 106.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 10625, we group it as 25 and 106.</p>

20 <p><strong>Step 2:</strong>Now, we need to find n whose square is<a>less than</a>or equal to 106. We can say n is ‘10’ because 10 x 10 = 100, which is less than 106. Now the<a>quotient</a>is 10, after subtracting 106 - 100, the<a>remainder</a>is 6.</p>

19 <p><strong>Step 2:</strong>Now, we need to find n whose square is<a>less than</a>or equal to 106. We can say n is ‘10’ because 10 x 10 = 100, which is less than 106. Now the<a>quotient</a>is 10, after subtracting 106 - 100, the<a>remainder</a>is 6.</p>

21 <p><strong>Step 3:</strong>Bring down 25 to make the new<a>dividend</a>625.</p>

20 <p><strong>Step 3:</strong>Bring down 25 to make the new<a>dividend</a>625.</p>

22 <p><strong>Step 4:</strong>The new<a>divisor</a>will be the sum of the old divisor and the quotient, so 10 + 10 = 20.</p>

21 <p><strong>Step 4:</strong>The new<a>divisor</a>will be the sum of the old divisor and the quotient, so 10 + 10 = 20.</p>

23 <p><strong>Step 5:</strong>We need to find n such that 20n x n ≤ 625. Let us consider n as 3. Now, 203 x 3 = 609.</p>

22 <p><strong>Step 5:</strong>We need to find n such that 20n x n ≤ 625. Let us consider n as 3. Now, 203 x 3 = 609.</p>

24 <p><strong>Step 6:</strong>Subtract 625 from 609, the difference is 16, and the quotient is 103.</p>

23 <p><strong>Step 6:</strong>Subtract 625 from 609, the difference is 16, and the quotient is 103.</p>

25 <p><strong>Step 7:</strong>Since there is no remainder, the process stops here, confirming that the square root of 10625 is 103.</p>

24 <p><strong>Step 7:</strong>Since there is no remainder, the process stops here, confirming that the square root of 10625 is 103.</p>

25 + <h2>Download Worksheets</h2>

26 <h3>Problem 1</h3>

27 <p>Can you help Max find the area of a square box if its side length is given as √10625?</p>

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

29 <p>The area of the square is 10625 square units.</p>

30 <h3>Explanation</h3>

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

32 <p>The side length is given as √10625.</p>

33 <p>Area of the square = side^2 = √10625 x √10625 = 103 x 103 = 10625</p>

34 <p>Therefore, the area of the square box is 10625 square units.</p>

35 <p>Well explained 👍</p>

36 <h3>Problem 2</h3>

37 <p>A square-shaped building measuring 10625 square feet is built; if each of the sides is √10625, what will be the square feet of half of the building?</p>

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

39 <p>5312.5 square feet</p>

40 <h3>Explanation</h3>

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

42 <p>Dividing 10625 by 2 = we get 5312.5</p>

43 <p>So half of the building measures 5312.5 square feet.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 3</h3>

46 <p>Calculate √10625 x 5.</p>

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

48 <p>515</p>

49 <h3>Explanation</h3>

50 <p>The first step is to find the square root of 10625, which is 103.</p>

51 <p>The second step is to multiply 103 by 5.</p>

52 <p>So 103 x 5 = 515.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

55 <p>What will be the square root of (10000 + 625)?</p>

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

57 <p>The square root is 103</p>

58 <h3>Explanation</h3>

59 <p>To find the square root, we need to find the sum of (10000 + 625). 10000 + 625 = 10625, and then √10625 = 103.</p>

60 <p>Therefore, the square root of (10000 + 625) is ±103.</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 5</h3>

63 <p>Find the perimeter of the rectangle if its length ‘l’ is √10625 units and the width ‘w’ is 38 units.</p>

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

65 <p>We find the perimeter of the rectangle as 282 units.</p>

66 <h3>Explanation</h3>

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

68 <p>Perimeter = 2 × (√10625 + 38) = 2 × (103 + 38) = 2 × 141 = 282 units.</p>

69 <p>Well explained 👍</p>

70 <h2>FAQ on Square Root of 10625</h2>

71 <h3>1.What is √10625 in its simplest form?</h3>

72 <p>The prime factorization of 10625 is 5 x 5 x 5 x 5 x 17, so the simplest form of √10625 = √(5^4 x 17) = 103.</p>

73 <h3>2.Mention the factors of 10625.</h3>

74 <p>Factors of 10625 are 1, 5, 25, 125, 425, 2125, 10625.</p>

75 <h3>3.Calculate the square of 10625.</h3>

76 <p>We get the square of 103 by multiplying the number by itself, that is 103 x 103 = 10609.</p>

77 <h3>4.Is 10625 a prime number?</h3>

78 <p>10625 is not a<a>prime number</a>, as it has more than two factors.</p>

79 <h3>5.10625 is divisible by?</h3>

80 <p>10625 has factors; those are 1, 5, 25, 125, 425, 2125, 10625.</p>

81 <h2>Important Glossaries for the Square Root of 10625</h2>

82 <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>

83 <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>

84 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 4, 9, and 16 are perfect squares. </li>

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

86 <li><strong>Long division method:</strong>A systematic method to find the square root of a number, especially useful for large numbers or non-perfect squares.</li>

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

88 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

91 <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>

92 <h3>Fun Fact</h3>

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