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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. The square root is used in fields like vehicle design and finance. Here, we will discuss the square root of 698.</p>

4 <h2>What is the Square Root of 698?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>squaring a<a>number</a>. Since 698 is not a<a>perfect square</a>, its square root is expressed in radical and exponential forms. In radical form, it is represented as √698, and in<a>exponential form</a>as (698)^(1/2). The approximate value of √698 is 26.41969, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>of two integers.</p>

6 <h2>Finding the Square Root of 698</h2>

7 <p>For perfect squares, the<a>prime factorization</a>method is used. However, for non-perfect squares, methods like<a>long division</a>and approximation are employed. Let's explore these methods: </p>

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

9 <li>Long division method </li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 698 by Prime Factorization Method</h2>

12 <p>Prime factorization involves expressing a number as a<a>product</a>of its prime<a>factors</a>. Here's how 698 is broken down:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 698:</p>

14 <p>Breaking it down, we get 2 x 349: 2^1 x 349^1</p>

15 <p><strong>Step 2:</strong>Since 698 is not a perfect square, the digits cannot be grouped into pairs. Thus, calculating the<a>square root</a>of 698 using prime factorization isn't possible.</p>

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18 <h2>Square Root of 698 by Long Division Method</h2>

17 <h2>Square Root of 698 by Long Division Method</h2>

19 <p>The long<a>division</a>method is used for non-perfect squares. Here's how to find the square root using this method, step by step:</p>

18 <p>The long<a>division</a>method is used for non-perfect squares. Here's how to find the square root using this method, step by step:</p>

20 <p><strong>Step 1:</strong>Group the numbers from right to left. For 698, group it as 98 and 6.</p>

19 <p><strong>Step 1:</strong>Group the numbers from right to left. For 698, group it as 98 and 6.</p>

21 <p><strong>Step 2:</strong>Find 'n' such that n^2 ≤ 6. n = 2 because 2 x 2 is<a>less than</a>or equal to 6. The<a>quotient</a>is 2, and the<a>remainder</a>is 2.</p>

20 <p><strong>Step 2:</strong>Find 'n' such that n^2 ≤ 6. n = 2 because 2 x 2 is<a>less than</a>or equal to 6. The<a>quotient</a>is 2, and the<a>remainder</a>is 2.</p>

22 <p><strong>Step 3:</strong>Bring down 98 to make a new<a>dividend</a>of 298. Add 2 (old<a>divisor</a>) to itself to get 4, the new divisor.</p>

21 <p><strong>Step 3:</strong>Bring down 98 to make a new<a>dividend</a>of 298. Add 2 (old<a>divisor</a>) to itself to get 4, the new divisor.</p>

23 <p><strong>Step 4:</strong>Find n such that 4n x n ≤ 298. Try n = 6, so 46 x 6 = 276.</p>

22 <p><strong>Step 4:</strong>Find n such that 4n x n ≤ 298. Try n = 6, so 46 x 6 = 276.</p>

24 <p><strong>Step 5:</strong>Subtract 276 from 298, leaving a remainder of 22. The quotient is 26.</p>

23 <p><strong>Step 5:</strong>Subtract 276 from 298, leaving a remainder of 22. The quotient is 26.</p>

25 <p><strong>Step 6:</strong>Since the remainder is less than the divisor, add a<a>decimal</a>point and two zeros to make the new dividend 2200.</p>

24 <p><strong>Step 6:</strong>Since the remainder is less than the divisor, add a<a>decimal</a>point and two zeros to make the new dividend 2200.</p>

26 <p><strong>Step 7:</strong>The new divisor is 529 because 529 x 4 = 2116, which is less than 2200.</p>

25 <p><strong>Step 7:</strong>The new divisor is 529 because 529 x 4 = 2116, which is less than 2200.</p>

27 <p><strong>Step 8:</strong>Subtract 2116 from 2200, leaving 84.</p>

26 <p><strong>Step 8:</strong>Subtract 2116 from 2200, leaving 84.</p>

28 <p><strong>Step 9:</strong>The quotient is now 26.4. Continue these steps to get a more precise square root value.</p>

27 <p><strong>Step 9:</strong>The quotient is now 26.4. Continue these steps to get a more precise square root value.</p>

29 <p>The square root of √698 is approximately 26.42.</p>

28 <p>The square root of √698 is approximately 26.42.</p>

30 <h2>Square Root of 698 by Approximation Method</h2>

29 <h2>Square Root of 698 by Approximation Method</h2>

31 <p>The approximation method finds square roots easily. Here’s how to approximate the square root of 698:</p>

30 <p>The approximation method finds square roots easily. Here’s how to approximate the square root of 698:</p>

32 <p><strong>Step 1:</strong>Identify the closest perfect squares to 698. 676 and 729 are nearby perfect squares. √698 falls between 26 and 27.</p>

31 <p><strong>Step 1:</strong>Identify the closest perfect squares to 698. 676 and 729 are nearby perfect squares. √698 falls between 26 and 27.</p>

33 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). For 698, use (698 - 676) / (729 - 676) = 22 / 53 ≈ 0.415 Adding this to the smaller square root, we get 26 + 0.415 = 26.415.</p>

32 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). For 698, use (698 - 676) / (729 - 676) = 22 / 53 ≈ 0.415 Adding this to the smaller square root, we get 26 + 0.415 = 26.415.</p>

34 <p>So, the square root of 698 is approximately 26.42.</p>

33 <p>So, the square root of 698 is approximately 26.42.</p>

35 <h2>Common Mistakes and How to Avoid Them in the Square Root of 698</h2>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 698</h2>

36 <p>Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's review common mistakes in detail.</p>

35 <p>Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's review common mistakes in detail.</p>

36 + <h2>Download Worksheets</h2>

37 <h3>Problem 1</h3>

38 <p>Can you help Max find the area of a square box if its side length is given as √698?</p>

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

40 <p>The area of the square is approximately 486.18 square units.</p>

41 <h3>Explanation</h3>

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

43 <p>The side length is √698.</p>

44 <p>Area = (√698)² ≈ 26.42 × 26.42 = 698.</p>

45 <p>Therefore, the area of the square box is approximately 698 square units.</p>

46 <p>Well explained 👍</p>

47 <h3>Problem 2</h3>

48 <p>A square-shaped building measuring 698 square feet is built; if each of the sides is √698, what will be the square feet of half of the building?</p>

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

50 <p>349 square feet.</p>

51 <h3>Explanation</h3>

52 <p>Since the building is square-shaped, divide the given area by 2.</p>

53 <p>Dividing 698 by 2 gives 349.</p>

54 <p>So half of the building measures 349 square feet.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 3</h3>

57 <p>Calculate √698 × 5.</p>

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

59 <p>Approximately 132.1.</p>

60 <h3>Explanation</h3>

61 <p>First, find the square root of 698, which is approximately 26.42.</p>

62 <p>Then multiply 26.42 by 5: 26.42 × 5 ≈ 132.1</p>

63 <p>Well explained 👍</p>

64 <h3>Problem 4</h3>

65 <p>What will be the square root of (698 + 2)?</p>

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

67 <p>The square root is approximately 26.46.</p>

68 <h3>Explanation</h3>

69 <p>To find the square root, sum (698 + 2) to get 700.</p>

70 <p>√700 ≈ 26.46.</p>

71 <p>Therefore, the square root of (698 + 2) is approximately ±26.46.</p>

72 <p>Well explained 👍</p>

73 <h3>Problem 5</h3>

74 <p>Find the perimeter of a rectangle if its length 'l' is √698 units and the width 'w' is 38 units.</p>

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

76 <p>The perimeter of the rectangle is approximately 129.84 units.</p>

77 <h3>Explanation</h3>

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

79 <p>Perimeter = 2 × (√698 + 38) ≈ 2 × (26.42 + 38) ≈ 2 × 64.42 ≈ 128.84 units.</p>

80 <p>Well explained 👍</p>

81 <h2>FAQ on Square Root of 698</h2>

82 <h3>1.What is √698 in its simplest form?</h3>

83 <p>The prime factorization of 698 is 2 × 349, so the simplest form of √698 is √(2 × 349).</p>

84 <h3>2.Mention the factors of 698.</h3>

85 <p>Factors of 698 are 1, 2, 349, and 698.</p>

86 <h3>3.Calculate the square of 698.</h3>

87 <p>To find the square of 698, multiply the number by itself: 698 × 698 = 487204.</p>

88 <h3>4.Is 698 a prime number?</h3>

89 <p>698 is not a<a>prime number</a>because it has more than two factors.</p>

90 <h3>5.698 is divisible by?</h3>

91 <p>698 is divisible by 1, 2, 349, and 698.</p>

92 <h2>Important Glossaries for the Square Root of 698</h2>

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

94 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction; for example, the square root of 698 is irrational.</li>

95 </ul><ul><li><strong>Decimal:</strong>A decimal is a number that includes a whole number and a fractional part, such as 26.42.</li>

96 </ul><ul><li><strong>Exponent:</strong>An exponent indicates how many times a number is multiplied by itself, such as ² in (698)^(1/2).</li>

97 </ul><ul><li><strong>Perimeter:</strong>The perimeter is the total distance around a two-dimensional shape, calculated by summing all side lengths.</li>

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

99 <p>▶</p>

100 <h2>Jaskaran Singh Saluja</h2>

101 <h3>About the Author</h3>

102 <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>

103 <h3>Fun Fact</h3>

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