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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 10.25.</p>

4 <h2>What is the Square Root of 10.25?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 10.25 is a<a>perfect square</a>. The square root of 10.25 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √10.25, whereas (10.25)^(1/2) in the exponential form. √10.25 = 3.2, 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 10.25</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for<a>decimal</a>perfect squares, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>

8 <ul><li>Long division method</li>

9 <li>Approximation method</li>

10 </ul><h2>Square Root of 10.25 by Long Division Method</h2>

11 <p>The<a>long division</a>method is particularly used for non-perfect square numbers and<a>decimal numbers</a>. In this method, we should check the grouping of digits for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>

12 <p><strong>Step 1:</strong>To begin with, consider the number 10.25. Place a decimal point and pair the digits before and after the decimal point.</p>

13 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 10. We can choose 3 because 3 × 3 = 9. Subtract 9 from 10, and bring down the next pair of digits, 25, making the new<a>dividend</a>125.</p>

14 <p><strong>Step 3:</strong>Double the current<a>quotient</a>(3), giving us 6, which will be our new<a>divisor</a>base.</p>

15 <p><strong>Step 4:</strong>Find a digit x such that 6x × x is less than or equal to 125. The suitable digit is 2, making the divisor 62 and the product 62 × 2 = 124.</p>

16 <p><strong>Step 5:</strong>Subtract 124 from 125, leaving a remainder of 1.</p>

17 <p>Since there are no more pairs of digits, the quotient, 3.2, is the square root of 10.25.</p>

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20 <h2>Square Root of 10.25 by Approximation Method</h2>

19 <h2>Square Root of 10.25 by Approximation Method</h2>

21 <p>Approximation method is another method for finding square roots; it is an easy method to approximate the square root of a given number. Now let us learn how to find the square root of 10.25 using the approximation method:</p>

20 <p>Approximation method is another method for finding square roots; it is an easy method to approximate the square root of a given number. Now let us learn how to find the square root of 10.25 using the approximation method:</p>

22 <p><strong>Step 1:</strong>Identify the perfect squares around 10.25. The closest perfect square less than 10.25 is 9, and the closest perfect square<a>greater than</a>10.25 is 16.</p>

21 <p><strong>Step 1:</strong>Identify the perfect squares around 10.25. The closest perfect square less than 10.25 is 9, and the closest perfect square<a>greater than</a>10.25 is 16.</p>

23 <p><strong>Step 2:</strong>Knowing that √9 = 3 and √16 = 4, we can see that √10.25 is between 3 and 4.</p>

22 <p><strong>Step 2:</strong>Knowing that √9 = 3 and √16 = 4, we can see that √10.25 is between 3 and 4.</p>

24 <p><strong>Step 3:</strong>Narrow down by approximation. Since 10.25 is closer to 9, we try 3.2. Calculate 3.2 × 3.2 = 10.24, which is very close.</p>

23 <p><strong>Step 3:</strong>Narrow down by approximation. Since 10.25 is closer to 9, we try 3.2. Calculate 3.2 × 3.2 = 10.24, which is very close.</p>

25 <p>Thus, the square root of 10.25 is approximately 3.2.</p>

24 <p>Thus, the square root of 10.25 is approximately 3.2.</p>

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 10.25</h2>

25 <h2>Common Mistakes and How to Avoid Them in the Square Root of 10.25</h2>

27 <p>Students often make mistakes while finding square roots, such as misunderstanding the concept of perfect squares and applying incorrect methods. Let us look at a few common mistakes students tend to make and how to avoid them in detail.</p>

26 <p>Students often make mistakes while finding square roots, such as misunderstanding the concept of perfect squares and applying incorrect methods. Let us look at a few common mistakes students tend to make and how to avoid them in detail.</p>

28 <h3>Problem 1</h3>

27 <h3>Problem 1</h3>

29 <p>Can you help Max find the area of a square box if its side length is given as √10.25?</p>

28 <p>Can you help Max find the area of a square box if its side length is given as √10.25?</p>

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

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

31 <p>The area of the square is 10.25 square units.</p>

30 <p>The area of the square is 10.25 square units.</p>

32 <h3>Explanation</h3>

31 <h3>Explanation</h3>

33 <p>The area of a square is side².</p>

32 <p>The area of a square is side².</p>

34 <p>The side length is given as √10.25.</p>

33 <p>The side length is given as √10.25.</p>

35 <p>Area of the square = side² = √10.25 × √10.25 = 3.2 × 3.2 = 10.25.</p>

34 <p>Area of the square = side² = √10.25 × √10.25 = 3.2 × 3.2 = 10.25.</p>

36 <p>Therefore, the area of the square box is 10.25 square units.</p>

35 <p>Therefore, the area of the square box is 10.25 square units.</p>

37 <p>Well explained 👍</p>

36 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

37 <h3>Problem 2</h3>

39 <p>A square-shaped garden measuring 10.25 square feet is built; if each of the sides is √10.25, what will be the square feet of half of the garden?</p>

38 <p>A square-shaped garden measuring 10.25 square feet is built; if each of the sides is √10.25, what will be the square feet of half of the garden?</p>

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

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

41 <p>5.125 square feet</p>

40 <p>5.125 square feet</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>We can determine half of the garden's area by dividing the given area by 2, as the garden is square-shaped.</p>

42 <p>We can determine half of the garden's area by dividing the given area by 2, as the garden is square-shaped.</p>

44 <p>Dividing 10.25 by 2, we get 5.125.</p>

43 <p>Dividing 10.25 by 2, we get 5.125.</p>

45 <p>So, half of the garden measures 5.125 square feet.</p>

44 <p>So, half of the garden measures 5.125 square feet.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

46 <h3>Problem 3</h3>

48 <p>Calculate √10.25 × 5.</p>

47 <p>Calculate √10.25 × 5.</p>

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

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

50 <p>16</p>

49 <p>16</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>The first step is to find the square root of 10.25, which is 3.2.</p>

51 <p>The first step is to find the square root of 10.25, which is 3.2.</p>

53 <p>The second step is to multiply 3.2 by 5.</p>

52 <p>The second step is to multiply 3.2 by 5.</p>

54 <p>So, 3.2 × 5 = 16.</p>

53 <p>So, 3.2 × 5 = 16.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

55 <h3>Problem 4</h3>

57 <p>What will be the square root of (6.25 + 4)?</p>

56 <p>What will be the square root of (6.25 + 4)?</p>

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

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

59 <p>The square root is 3.2.</p>

58 <p>The square root is 3.2.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>To find the square root, we need to find the sum of (6.25 + 4). 6.25 + 4 = 10.25, and then 10.25 = 3.2.</p>

60 <p>To find the square root, we need to find the sum of (6.25 + 4). 6.25 + 4 = 10.25, and then 10.25 = 3.2.</p>

62 <p>Therefore, the square root of (6.25 + 4) is ±3.2.</p>

61 <p>Therefore, the square root of (6.25 + 4) is ±3.2.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

63 <h3>Problem 5</h3>

65 <p>Find the perimeter of a rectangle if its length ‘l’ is √10.25 units and the width ‘w’ is 5 units.</p>

64 <p>Find the perimeter of a rectangle if its length ‘l’ is √10.25 units and the width ‘w’ is 5 units.</p>

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

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

67 <p>The perimeter of the rectangle is 16.4 units.</p>

66 <p>The perimeter of the rectangle is 16.4 units.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

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

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

70 <p>Perimeter = 2 × (√10.25 + 5) = 2 × (3.2 + 5) = 2 × 8.2 = 16.4 units.</p>

69 <p>Perimeter = 2 × (√10.25 + 5) = 2 × (3.2 + 5) = 2 × 8.2 = 16.4 units.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h2>FAQ on Square Root of 10.25</h2>

71 <h2>FAQ on Square Root of 10.25</h2>

73 <h3>1.What is √10.25 in its simplest form?</h3>

72 <h3>1.What is √10.25 in its simplest form?</h3>

74 <p>√10.25 is already in its simplest form, as it is a perfect square. Its square root is 3.2.</p>

73 <p>√10.25 is already in its simplest form, as it is a perfect square. Its square root is 3.2.</p>

75 <h3>2.Can 10.25 be expressed as a fraction?</h3>

74 <h3>2.Can 10.25 be expressed as a fraction?</h3>

76 <p>Yes, 10.25 can be expressed as a<a>fraction</a>: 10.25 = 41/4.</p>

75 <p>Yes, 10.25 can be expressed as a<a>fraction</a>: 10.25 = 41/4.</p>

77 <h3>3.Calculate the square of 3.2.</h3>

76 <h3>3.Calculate the square of 3.2.</h3>

78 <p>We get the square of 3.2 by multiplying the number by itself, which is 3.2 × 3.2 = 10.24.</p>

77 <p>We get the square of 3.2 by multiplying the number by itself, which is 3.2 × 3.2 = 10.24.</p>

79 <h3>4.Is 10.25 a rational number?</h3>

78 <h3>4.Is 10.25 a rational number?</h3>

80 <p>Yes, 10.25 is a rational number because it can be expressed as a fraction, 41/4.</p>

79 <p>Yes, 10.25 is a rational number because it can be expressed as a fraction, 41/4.</p>

81 <h3>5.What is the principal square root of 10.25?</h3>

80 <h3>5.What is the principal square root of 10.25?</h3>

82 <p>The principal square root of 10.25 is 3.2.</p>

81 <p>The principal square root of 10.25 is 3.2.</p>

83 <h2>Important Glossaries for the Square Root of 10.25</h2>

82 <h2>Important Glossaries for the Square Root of 10.25</h2>

84 <ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 3.2² = 10.24, and the inverse of the square is the square root, so √10.25 = 3.2. </li>

83 <ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 3.2² = 10.24, and the inverse of the square is the square root, so √10.25 = 3.2. </li>

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

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

86 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer or a rational number. Example: 10.25 is a perfect square because √10.25 = 3.2. </li>

85 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer or a rational number. Example: 10.25 is a perfect square because √10.25 = 3.2. </li>

87 <li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals. </li>

86 <li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals. </li>

88 <li><strong>Long division method:</strong>A step-by-step process used to find the square root of a number, especially useful for numbers that are not perfect squares or for decimal numbers.</li>

87 <li><strong>Long division method:</strong>A step-by-step process used to find the square root of a number, especially useful for numbers that are not perfect squares or for decimal numbers.</li>

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

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

90 <p>▶</p>

89 <p>▶</p>

91 <h2>Jaskaran Singh Saluja</h2>

90 <h2>Jaskaran Singh Saluja</h2>

92 <h3>About the Author</h3>

91 <h3>About the Author</h3>

93 <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 <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>

94 <h3>Fun Fact</h3>

93 <h3>Fun Fact</h3>

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

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