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1 - <p>529 Learners</p>

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

3 <p>Square root is simply a number value that when multiplied with itself gives the original number. We apply square roots when we make financial estimations and solve practical problems in geometry.</p>

4 <h2>What is the square root of 361?</h2>

5 <p>The<a>square</a>root is the<a>number</a>that gives the original number when squared. </p>

6 <p>√361 = 19,</p>

7 <p>in<a>exponential form</a>it is written as √361 =.3611/2 =19</p>

8 <p>In this article we will learn more about the square root of 361, how to find it and common mistakes one may make when trying to find the square root. </p>

9 <h2>Finding the square root of 361</h2>

10 <p>To find the<a>square root</a>of a number of students learn many methods. When a number is a<a>perfect square</a>and the process of finding square root is simple. </p>

11 <h3>Square root using the prime factorization method</h3>

12 <p>Breakdown 361 into<a>prime factors</a>, group them, and the result is the square root. </p>

13 <p><strong>Step 1:</strong>Prime factorize </p>

14 <p>361 = 19×19</p>

15 <p><strong>Step 2:</strong>Group factors in pairs</p>

16 <p>√361 = √19×19</p>

17 <p><strong>Step 3:</strong>Multiply factors to find the square root</p>

18 <p> √361 = 19 </p>

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21 <h3>Square root of 361 using the division method</h3>

20 <h3>Square root of 361 using the division method</h3>

22 <p>Pair the digits, begin with the largest square and continue the<a>subtraction</a>and<a>division</a>till we find the result which is the square root of the number. </p>

21 <p>Pair the digits, begin with the largest square and continue the<a>subtraction</a>and<a>division</a>till we find the result which is the square root of the number. </p>

23 <p><strong>Step 1:</strong>Pair 361</p>

22 <p><strong>Step 1:</strong>Pair 361</p>

24 <p>361 → (3)(61) </p>

23 <p>361 → (3)(61) </p>

25 <p><strong>Step 2:</strong>pick a number whose square is ≤ 3, 12=1</p>

24 <p><strong>Step 2:</strong>pick a number whose square is ≤ 3, 12=1</p>

26 <p>- 1 is the<a>quotient</a>. </p>

25 <p>- 1 is the<a>quotient</a>. </p>

27 <p>- Subtract the numbers, 3-1=2. </p>

26 <p>- Subtract the numbers, 3-1=2. </p>

28 <p>- Bring down the numbers 61 next to the<a>remainder</a>, we get 261.</p>

27 <p>- Bring down the numbers 61 next to the<a>remainder</a>, we get 261.</p>

29 <p><strong>Step 3:</strong>double quotient and use it as the first digit of the new<a>divisor</a>’s</p>

28 <p><strong>Step 3:</strong>double quotient and use it as the first digit of the new<a>divisor</a>’s</p>

30 <p>- Double 1</p>

29 <p>- Double 1</p>

31 <p>- Now find the digit x in a way that 2x×x ≤ 261 </p>

30 <p>- Now find the digit x in a way that 2x×x ≤ 261 </p>

32 <p>- x is 9, 29×9 = 261.</p>

31 <p>- x is 9, 29×9 = 261.</p>

33 <p><strong>Step 4:</strong>Now find the final quotient </p>

32 <p><strong>Step 4:</strong>Now find the final quotient </p>

34 <p>- The quotient we are left with 19, the square root of √361</p>

33 <p>- The quotient we are left with 19, the square root of √361</p>

35 <p>The result; √361 = 19</p>

34 <p>The result; √361 = 19</p>

36 <h3>Square root of 361 using the repeated subtraction method</h3>

35 <h3>Square root of 361 using the repeated subtraction method</h3>

37 <p>Subtract<a>odd numbers</a>that are consecutive, keep track of the number of subtractions until we reach 0. </p>

36 <p>Subtract<a>odd numbers</a>that are consecutive, keep track of the number of subtractions until we reach 0. </p>

38 <p><strong>Step 1:</strong>Start the subtraction of consecutive odd numbers from 361, starting from 1. </p>

37 <p><strong>Step 1:</strong>Start the subtraction of consecutive odd numbers from 361, starting from 1. </p>

39 <p><strong>Step 2:</strong>Maintain a count of the number of the subtractions performed</p>

38 <p><strong>Step 2:</strong>Maintain a count of the number of the subtractions performed</p>

40 <p>361-1= 360</p>

39 <p>361-1= 360</p>

41 <p>360-3 =357</p>

40 <p>360-3 =357</p>

42 <p>357-5=352</p>

41 <p>357-5=352</p>

43 <p>352-7=345</p>

42 <p>352-7=345</p>

44 <p><strong>Step 3:</strong>Continue the subtraction until the remainder is 0.</p>

43 <p><strong>Step 3:</strong>Continue the subtraction until the remainder is 0.</p>

45 <p>After performing 19 subtractions, the remainder is 0. The square root of the number is 19. </p>

44 <p>After performing 19 subtractions, the remainder is 0. The square root of the number is 19. </p>

46 <p>The result; √361 = 19 </p>

45 <p>The result; √361 = 19 </p>

47 <h2>Common mistakes and how to avoid them in square root of 361</h2>

46 <h2>Common mistakes and how to avoid them in square root of 361</h2>

48 <p>Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them. </p>

47 <p>Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them. </p>

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49 <h3>Problem 1</h3>

50 <p>If x=√361 = solve x²+4x+5.</p>

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

52 <p>We know √361=19,</p>

53 <p>so x=19. Now substitute x into the expression:</p>

54 <p>x2+4x+5</p>

55 <p>=192+4(19)+5</p>

56 <p>=361+76+5</p>

57 <p>=442 </p>

58 <h3>Explanation</h3>

59 <p>First, square x, then substitute into the equation to get the result. </p>

60 <p>Well explained 👍</p>

61 <h3>Problem 2</h3>

62 <p>Determine whether 361 is a prime or composite number using its square root.</p>

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

64 <p>The square root of 361 is ±19, meaning 361 is the square of 19. Since 19 is a prime number, and 361 has factors other than 1 and 361 (i.e.,19×19), 361 is a composite number.</p>

65 <h3>Explanation</h3>

66 <p>A composite number has more than two factors. Since 361 has a factorization involving 19, it is not a prime number.</p>

67 <p>Well explained 👍</p>

68 <h3>Problem 3</h3>

69 <p>Find the difference between the square roots of 400 and 361</p>

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

71 <p> First, find the square roots of 400 and 361:</p>

72 <p>√400= 20 and √361=19 </p>

73 <p>Now find the difference:</p>

74 <p>20-19=1 </p>

75 <h3>Explanation</h3>

76 <p> The square roots of 400 and 361 are 20 and 19, respectively, and their difference is 1. </p>

77 <p>Well explained 👍</p>

78 <h2>FAQs on the Square root of 361</h2>

79 <h3>1.Is 361 irrational?</h3>

80 <h3>2.Is 361 a cube root?</h3>

81 <p>361 does not have an integer<a>cube</a>root. The cube root of 361 does not contain<a>powers</a>of 3 and is also irrational. </p>

82 <h3>3.Is 5√7 irrational?</h3>

83 <p>Yes, 5√7 is an irrational number. A non-integer multiple of a number, say √7, that is irrational remains irrational. </p>

84 <h3>4.What is the square root of 8?</h3>

85 <p> the square root of 8 is an irrational number, approximately 2.828.</p>

86 <h3>5.Is 2025 a perfect square?</h3>

87 <p>- 45 is the square root of 2025 making the number a perfect square. </p>

88 <h2>Important glossaries for the square root of 361</h2>

89 <ul><li><strong>Prime numbers -</strong>A number that has only two factors, 1 and the number itself. Prime numbers up to 10 are - 2,3,5,7.</li>

90 </ul><ul><li><strong>Integer -</strong>A number between zero and infinite, that can be positive or negative, fraction or decimal. </li>

91 </ul><ul><li><strong>Perfect square number -</strong>a number whose square root has no decimal places in them. For example, the square root of 3600. </li>

92 </ul><ul><li><strong>Non-perfect square numbers -</strong>A number whose square has a fraction or decimal in its result. For example, square root of 117. </li>

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

94 <p>▶</p>

95 <h2>Jaskaran Singh Saluja</h2>

96 <h3>About the Author</h3>

97 <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 <h3>Fun Fact</h3>

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