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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 1.69</p>

4 <h2>What is the Square Root of 1.69?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1.69 is a<a>perfect square</a>. The square root of 1.69 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1.69, whereas (1.69)^(1/2) in the<a>exponential form</a>. √1.69 = 1.3, 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 1.69</h2>

7 <p>The<a>prime factorization</a>method is typically used for perfect square numbers. Since 1.69 is a perfect square, we can use simple<a>arithmetic</a>to find its<a>square root</a>. Other methods like the long-<a>division</a>method and approximation are not needed in this case. Let us now learn how we can find the square root:</p>

8 <ul><li>Arithmetic method</li>

9 <li>Verification method</li>

10 </ul><h2>Square Root of 1.69 by Arithmetic Method</h2>

11 <p>By simple arithmetic, we can determine that 1.69 is the square of 1.3.</p>

12 <p><strong>Step 1:</strong>Recognize the<a>decimal</a>nature of 1.69 and express it as a<a>fraction</a>: 1.69 = 169/100.</p>

13 <p><strong>Step 2:</strong>Simplify the<a>expression</a>by taking the square root of both the<a>numerator</a>and the<a>denominator</a>: √(169/100) = √169 / √100 = 13/10 = 1.3.</p>

14 <p>Thus, the square root of 1.69 is 1.3.</p>

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17 <h2>Square Root of 1.69 by Verification Method</h2>

16 <h2>Square Root of 1.69 by Verification Method</h2>

18 <p>Verification ensures the correctness of our arithmetic approach. By squaring 1.3, we can validate our result.</p>

17 <p>Verification ensures the correctness of our arithmetic approach. By squaring 1.3, we can validate our result.</p>

19 <p><strong>Step 1:</strong>Square 1.3 to verify: 1.3 × 1.3 = 1.69.</p>

18 <p><strong>Step 1:</strong>Square 1.3 to verify: 1.3 × 1.3 = 1.69.</p>

20 <p><strong>Step 2:</strong>Since our squared result is 1.69, the square root of 1.69 is indeed 1.3.</p>

19 <p><strong>Step 2:</strong>Since our squared result is 1.69, the square root of 1.69 is indeed 1.3.</p>

21 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1.69</h2>

20 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1.69</h2>

22 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or miscalculating decimal places. Now let us look at a few of those mistakes that students tend to make in detail.</p>

21 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or miscalculating decimal places. Now let us look at a few of those mistakes that students tend to make in detail.</p>

23 <h3>Problem 1</h3>

22 <h3>Problem 1</h3>

24 <p>Can you help Max find the area of a square box if its side length is given as √1.69?</p>

23 <p>Can you help Max find the area of a square box if its side length is given as √1.69?</p>

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

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

26 <p>The area of the square is 1.69 square units.</p>

25 <p>The area of the square is 1.69 square units.</p>

27 <h3>Explanation</h3>

26 <h3>Explanation</h3>

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

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

29 <p>The side length is given as √1.69.</p>

28 <p>The side length is given as √1.69.</p>

30 <p>Area of the square = side^2 = √1.69 × √1.69 = 1.3 × 1.3 = 1.69.</p>

29 <p>Area of the square = side^2 = √1.69 × √1.69 = 1.3 × 1.3 = 1.69.</p>

31 <p>Therefore, the area of the square box is 1.69 square units.</p>

30 <p>Therefore, the area of the square box is 1.69 square units.</p>

32 <p>Well explained 👍</p>

31 <p>Well explained 👍</p>

33 <h3>Problem 2</h3>

32 <h3>Problem 2</h3>

34 <p>A square-shaped garden measures 1.69 square meters; if each of the sides is √1.69, what will be the square meters of half of the garden?</p>

33 <p>A square-shaped garden measures 1.69 square meters; if each of the sides is √1.69, what will be the square meters of half of the garden?</p>

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

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

36 <p>0.845 square meters</p>

35 <p>0.845 square meters</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

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

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

39 <p>Dividing 1.69 by 2 = 0.845</p>

38 <p>Dividing 1.69 by 2 = 0.845</p>

40 <p>So half of the garden measures 0.845 square meters.</p>

39 <p>So half of the garden measures 0.845 square meters.</p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 3</h3>

41 <h3>Problem 3</h3>

43 <p>Calculate √1.69 × 5.</p>

42 <p>Calculate √1.69 × 5.</p>

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

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

45 <p>6.5</p>

44 <p>6.5</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>The first step is to find the square root of 1.69, which is 1.3.</p>

46 <p>The first step is to find the square root of 1.69, which is 1.3.</p>

48 <p>The second step is to multiply 1.3 with 5.</p>

47 <p>The second step is to multiply 1.3 with 5.</p>

49 <p>So 1.3 × 5 = 6.5.</p>

48 <p>So 1.3 × 5 = 6.5.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 4</h3>

50 <h3>Problem 4</h3>

52 <p>What will be the square root of (0.69 + 1)?</p>

51 <p>What will be the square root of (0.69 + 1)?</p>

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

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

54 <p>The square root is 1.3.</p>

53 <p>The square root is 1.3.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>To find the square root, we need to find the sum of (0.69 + 1).</p>

55 <p>To find the square root, we need to find the sum of (0.69 + 1).</p>

57 <p>0.69 + 1 = 1.69, and then √1.69 = 1.3.</p>

56 <p>0.69 + 1 = 1.69, and then √1.69 = 1.3.</p>

58 <p>Therefore, the square root of (0.69 + 1) is ±1.3.</p>

57 <p>Therefore, the square root of (0.69 + 1) is ±1.3.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 5</h3>

59 <h3>Problem 5</h3>

61 <p>Find the perimeter of the rectangle if its length 'l' is √1.69 units and the width 'w' is 0.3 units.</p>

60 <p>Find the perimeter of the rectangle if its length 'l' is √1.69 units and the width 'w' is 0.3 units.</p>

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

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

63 <p>We find the perimeter of the rectangle as 3.2 units.</p>

62 <p>We find the perimeter of the rectangle as 3.2 units.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

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

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

66 <p>Perimeter = 2 × (√1.69 + 0.3)</p>

65 <p>Perimeter = 2 × (√1.69 + 0.3)</p>

67 <p>= 2 × (1.3 + 0.3)</p>

66 <p>= 2 × (1.3 + 0.3)</p>

68 <p>= 2 × 1.6</p>

67 <p>= 2 × 1.6</p>

69 <p>= 3.2 units.</p>

68 <p>= 3.2 units.</p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQ on Square Root of 1.69</h2>

70 <h2>FAQ on Square Root of 1.69</h2>

72 <h3>1.What is √1.69 in its simplest form?</h3>

71 <h3>1.What is √1.69 in its simplest form?</h3>

73 <p>The simplest form of √1.69 is 1.3.</p>

72 <p>The simplest form of √1.69 is 1.3.</p>

74 <h3>2.Can 1.69 be expressed as a fraction?</h3>

73 <h3>2.Can 1.69 be expressed as a fraction?</h3>

75 <p>Yes, 1.69 can be expressed as 169/100.</p>

74 <p>Yes, 1.69 can be expressed as 169/100.</p>

76 <h3>3.Calculate the square of 1.69.</h3>

75 <h3>3.Calculate the square of 1.69.</h3>

77 <p>To find the square of 1.69, multiply it by itself: 1.69 × 1.69 = 2.8561.</p>

76 <p>To find the square of 1.69, multiply it by itself: 1.69 × 1.69 = 2.8561.</p>

78 <h3>4.Is 1.69 a rational number?</h3>

77 <h3>4.Is 1.69 a rational number?</h3>

79 <p>Yes, 1.69 is a rational number because it can be expressed as the fraction 169/100.</p>

78 <p>Yes, 1.69 is a rational number because it can be expressed as the fraction 169/100.</p>

80 <h3>5.What is the decimal representation of the square root of 1.69?</h3>

79 <h3>5.What is the decimal representation of the square root of 1.69?</h3>

81 <h2>Important Glossaries for the Square Root of 1.69</h2>

80 <h2>Important Glossaries for the Square Root of 1.69</h2>

82 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 1.3^2 = 1.69, and thus the square root of 1.69 is 1.3. </li>

81 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 1.3^2 = 1.69, and thus the square root of 1.69 is 1.3. </li>

83 <li><strong>Rational number:</strong>A rational number can be expressed as the quotient of two integers, where the denominator is not zero. For example, 1.3 is rational because it is 13/10. </li>

82 <li><strong>Rational number:</strong>A rational number can be expressed as the quotient of two integers, where the denominator is not zero. For example, 1.3 is rational because it is 13/10. </li>

84 <li><strong>Perfect square:</strong>A number that is the square of an integer or a rational number. For example, 1.69 is a perfect square because it is (1.3)^2. </li>

83 <li><strong>Perfect square:</strong>A number that is the square of an integer or a rational number. For example, 1.69 is a perfect square because it is (1.3)^2. </li>

85 <li><strong>Decimal:</strong>A number that has a whole number and a fractional part separated by a decimal point, such as 1.3. </li>

84 <li><strong>Decimal:</strong>A number that has a whole number and a fractional part separated by a decimal point, such as 1.3. </li>

86 <li><strong>Principal square root:</strong>The non-negative square root of a number. For instance, the principal square root of 1.69 is 1.3.</li>

85 <li><strong>Principal square root:</strong>The non-negative square root of a number. For instance, the principal square root of 1.69 is 1.3.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

88 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

89 <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>

90 <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>

91 <h3>Fun Fact</h3>

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

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