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1 - <p>273 Learners</p>

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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. Square roots are used in fields like engineering, finance, and more. Here, we will discuss the square root of 0.0008.</p>

4 <h2>What is the Square Root of 0.0008?</h2>

5 <p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. Since 0.0008 is not a<a>perfect square</a>, its square root can be expressed in radical and exponential forms. In radical form, it is √0.0008, and in<a>exponential form</a>, it is (0.0008)^(1/2). The square root of 0.0008 is approximately 0.028284, which is an<a>irrational number</a>because it cannot be expressed as a simple<a>fraction</a>.</p>

6 <h2>Finding the Square Root of 0.0008</h2>

7 <p>For perfect squares, the<a>prime factorization</a>method is used, but for non-perfect squares like 0.0008, methods such as<a>long division</a>and approximation are more appropriate.</p>

8 <p>Let's explore these methods: </p>

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

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 0.0008 by Long Division Method</h2>

12 <p>The long<a>division</a>method is useful for non-perfect squares. Here's how to find the<a>square root</a>of a number using this method:</p>

13 <p><strong>Step 1:</strong>Start by pairing digits from right to left. For 0.0008, group as 08.</p>

14 <p><strong>Step 2:</strong>Determine the largest number whose square is<a>less than</a>or equal to 8. Here, 2 works because 2² = 4. The<a>quotient</a>is 2, and the<a>remainder</a>is 8 - 4 = 4.</p>

15 <p><strong>Step 3:</strong>Bring down two zeros, making the new<a>dividend</a>400. Double the quotient (2), giving us 4.</p>

16 <p><strong>Step 4:</strong>Find n such that (4n) × n ≤ 400. If n = 7, (47) × 7 = 329.</p>

17 <p><strong>Step 5:</strong>Subtract 329 from 400, leaving 71.</p>

18 <p><strong>Step 6:</strong>Add two zeros to make it 7100 and repeat the process until you achieve the desired precision.</p>

19 <p>The square root of 0.0008 is approximately 0.028284.</p>

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22 <h2>Square Root of 0.0008 by Approximation Method</h2>

21 <h2>Square Root of 0.0008 by Approximation Method</h2>

23 <p>The approximation method provides a straightforward way to find square roots. Here's how to approximate the square root of 0.0008:</p>

22 <p>The approximation method provides a straightforward way to find square roots. Here's how to approximate the square root of 0.0008:</p>

24 <p><strong>Step 1:</strong>Identify the perfect squares closest to 0.0008. The closest are 0.0004 (0.02²) and 0.0016 (0.04²). Thus, √0.0008 is between 0.02 and 0.04.</p>

23 <p><strong>Step 1:</strong>Identify the perfect squares closest to 0.0008. The closest are 0.0004 (0.02²) and 0.0016 (0.04²). Thus, √0.0008 is between 0.02 and 0.04.</p>

25 <p><strong>Step 2:</strong>Use interpolation: (Number - Lower perfect square) / (Upper perfect square - Lower perfect square). For example: (0.0008 - 0.0004) / (0.0016 - 0.0004) = 0.4 / 1.2 = 0.3333.</p>

24 <p><strong>Step 2:</strong>Use interpolation: (Number - Lower perfect square) / (Upper perfect square - Lower perfect square). For example: (0.0008 - 0.0004) / (0.0016 - 0.0004) = 0.4 / 1.2 = 0.3333.</p>

26 <p><strong>Step 3:</strong>Add this to the lower bound: 0.02 + 0.3333(0.02) = 0.026666.</p>

25 <p><strong>Step 3:</strong>Add this to the lower bound: 0.02 + 0.3333(0.02) = 0.026666.</p>

27 <p>Refining further yields an approximation of 0.028284.</p>

26 <p>Refining further yields an approximation of 0.028284.</p>

28 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 0.0008</h2>

27 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 0.0008</h2>

29 <p>Mistakes occur when calculating square roots, such as forgetting negative roots or misusing the long division method. Here are some mistakes and tips to avoid them:</p>

28 <p>Mistakes occur when calculating square roots, such as forgetting negative roots or misusing the long division method. Here are some mistakes and tips to avoid them:</p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>Can you help Max find the area of a square box if its side length is √0.0005?</p>

30 <p>Can you help Max find the area of a square box if its side length is √0.0005?</p>

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

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

33 <p>The area of the square is 0.0005 square units.</p>

32 <p>The area of the square is 0.0005 square units.</p>

34 <h3>Explanation</h3>

33 <h3>Explanation</h3>

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

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

36 <p>The side length is given as √0.0005.</p>

35 <p>The side length is given as √0.0005.</p>

37 <p>Area of the square = side² = √0.0005 × √0.0005</p>

36 <p>Area of the square = side² = √0.0005 × √0.0005</p>

38 <p>= 0.02236 × 0.02236 = 0.0005</p>

37 <p>= 0.02236 × 0.02236 = 0.0005</p>

39 <p>Therefore, the area of the square box is 0.0005 square units.</p>

38 <p>Therefore, the area of the square box is 0.0005 square units.</p>

40 <p>Well explained 👍</p>

39 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

40 <h3>Problem 2</h3>

42 <p>A square-shaped sheet measuring 0.0008 square meters is cut; if each of the sides is √0.0008, what will be the square meters of half of the sheet?</p>

41 <p>A square-shaped sheet measuring 0.0008 square meters is cut; if each of the sides is √0.0008, what will be the square meters of half of the sheet?</p>

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

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

44 <p>0.0004 square meters</p>

43 <p>0.0004 square meters</p>

45 <h3>Explanation</h3>

44 <h3>Explanation</h3>

46 <p>Divide the given area by 2 since the sheet is square-shaped.</p>

45 <p>Divide the given area by 2 since the sheet is square-shaped.</p>

47 <p>Dividing 0.0008 by 2 = 0.0004</p>

46 <p>Dividing 0.0008 by 2 = 0.0004</p>

48 <p>So half of the sheet measures 0.0004 square meters.</p>

47 <p>So half of the sheet measures 0.0004 square meters.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

49 <h3>Problem 3</h3>

51 <p>Calculate √0.0008 × 5.</p>

50 <p>Calculate √0.0008 × 5.</p>

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

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

53 <p>0.14142</p>

52 <p>0.14142</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>First, find the square root of 0.0008, which is approximately 0.028284.</p>

54 <p>First, find the square root of 0.0008, which is approximately 0.028284.</p>

56 <p>Then multiply 0.028284 by 5. So, 0.028284 × 5 = 0.14142</p>

55 <p>Then multiply 0.028284 by 5. So, 0.028284 × 5 = 0.14142</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

57 <h3>Problem 4</h3>

59 <p>What will be the square root of (0.0005 + 0.0003)?</p>

58 <p>What will be the square root of (0.0005 + 0.0003)?</p>

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

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

61 <p>The square root is approximately 0.028284.</p>

60 <p>The square root is approximately 0.028284.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>Find the sum of 0.0005 + 0.0003, which equals 0.0008.</p>

62 <p>Find the sum of 0.0005 + 0.0003, which equals 0.0008.</p>

64 <p>The square root of 0.0008 is approximately 0.028284.</p>

63 <p>The square root of 0.0008 is approximately 0.028284.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

65 <h3>Problem 5</h3>

67 <p>Find the perimeter of a rectangle if its length ‘l’ is √0.0005 units and the width ‘w’ is 0.01 units.</p>

66 <p>Find the perimeter of a rectangle if its length ‘l’ is √0.0005 units and the width ‘w’ is 0.01 units.</p>

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

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

69 <p>The perimeter of the rectangle is approximately 0.06472 units.</p>

68 <p>The perimeter of the rectangle is approximately 0.06472 units.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

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

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

72 <p>Perimeter = 2 × (√0.0005 + 0.01)</p>

71 <p>Perimeter = 2 × (√0.0005 + 0.01)</p>

73 <p>= 2 × (0.02236 + 0.01)</p>

72 <p>= 2 × (0.02236 + 0.01)</p>

74 <p>= 2 × 0.03236</p>

73 <p>= 2 × 0.03236</p>

75 <p>= 0.06472 units.</p>

74 <p>= 0.06472 units.</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h2>FAQ on Square Root of 0.0008</h2>

76 <h2>FAQ on Square Root of 0.0008</h2>

78 <h3>1.What is √0.0008 in its simplest form?</h3>

77 <h3>1.What is √0.0008 in its simplest form?</h3>

79 <p>The number 0.0008 can be expressed as 8 x 10^(-4).</p>

78 <p>The number 0.0008 can be expressed as 8 x 10^(-4).</p>

80 <p>The simplest form of √0.0008 = √(8 x 10^(-4)).</p>

79 <p>The simplest form of √0.0008 = √(8 x 10^(-4)).</p>

81 <h3>2.What are the factors of 0.0008?</h3>

80 <h3>2.What are the factors of 0.0008?</h3>

82 <p>Factors of 0.0008 include 1, 2, 4, 8, 0.1, 0.2, 0.4, and 0.8.</p>

81 <p>Factors of 0.0008 include 1, 2, 4, 8, 0.1, 0.2, 0.4, and 0.8.</p>

83 <h3>3.Calculate the square of 0.0008.</h3>

82 <h3>3.Calculate the square of 0.0008.</h3>

84 <p>To find the square of 0.0008, multiply it by itself: 0.0008 × 0.0008 = 0.00000064.</p>

83 <p>To find the square of 0.0008, multiply it by itself: 0.0008 × 0.0008 = 0.00000064.</p>

85 <h3>4.Is 0.0008 a rational number?</h3>

84 <h3>4.Is 0.0008 a rational number?</h3>

86 <p>Yes, 0.0008 is a<a>rational number</a>because it can be expressed as a fraction (8/10000).</p>

85 <p>Yes, 0.0008 is a<a>rational number</a>because it can be expressed as a fraction (8/10000).</p>

87 <h3>5.Is 0.0008 divisible by 0.2?</h3>

86 <h3>5.Is 0.0008 divisible by 0.2?</h3>

88 <p>No, 0.0008 is not divisible by 0.2 because 0.0008 ÷ 0.2 is not an<a>integer</a>.</p>

87 <p>No, 0.0008 is not divisible by 0.2 because 0.0008 ÷ 0.2 is not an<a>integer</a>.</p>

89 <h2>Important Glossaries for the Square Root of 0.0008</h2>

88 <h2>Important Glossaries for the Square Root of 0.0008</h2>

90 <ul><li><strong>Square root:</strong>The square root is the inverse operation of squaring a number. For example, 4² = 16, so √16 = 4. </li>

89 <ul><li><strong>Square root:</strong>The square root is the inverse operation of squaring a number. For example, 4² = 16, so √16 = 4. </li>

91 <li><strong>Irrational number:</strong>A number that cannot be expressed as a simple fraction, such as the square root of a non-perfect square. </li>

90 <li><strong>Irrational number:</strong>A number that cannot be expressed as a simple fraction, such as the square root of a non-perfect square. </li>

92 <li><strong>Approximation:</strong>The process of finding a value close to the actual value. For example, √0.0008 ≈ 0.028284. </li>

91 <li><strong>Approximation:</strong>The process of finding a value close to the actual value. For example, √0.0008 ≈ 0.028284. </li>

93 <li><strong>Decimal:</strong>A numerical value with a fractional part, represented with a dot, such as 0.03, 0.25. </li>

92 <li><strong>Decimal:</strong>A numerical value with a fractional part, represented with a dot, such as 0.03, 0.25. </li>

94 <li><strong>Long division method:</strong>A technique used to find the square root of non-perfect squares through successive approximations.</li>

93 <li><strong>Long division method:</strong>A technique used to find the square root of non-perfect squares through successive approximations.</li>

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

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

96 <p>▶</p>

95 <p>▶</p>

97 <h2>Jaskaran Singh Saluja</h2>

96 <h2>Jaskaran Singh Saluja</h2>

98 <h3>About the Author</h3>

97 <h3>About the Author</h3>

99 <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>

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>

100 <h3>Fun Fact</h3>

99 <h3>Fun Fact</h3>

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

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