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

3 <p>The square root of 49 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y × y, the result is 49. It contains both positive and a negative root, where the positive root is called the principal square root.</p>

4 <h2>What Is the Square Root of 49?</h2>

5 <p>The<a>square</a>root of 49 is ±7. The positive value, 7 is the solution of the<a>equation</a>x2 = 49. As defined, the square root is just the inverse of squaring a<a>number</a>, so, squaring 7 will result in 49. The square root of 49 is expressed as √49 in radical form, where the ‘√’ sign is called “radical” sign. In<a>exponential form</a>, it is written as (49)1/2 </p>

6 <h2>Finding the Square Root of 49</h2>

7 <p>We can find the<a>square root</a>of 49 through various methods. They are:</p>

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

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

10 </ul><ul><li>Subtraction method</li>

11 </ul><h3>Square Root of 49 By Prime Factorization Method</h3>

12 <p>The<a>prime factorization</a>of 49 involves breaking down a number into its<a>factors</a>. Divide 49 by<a>prime numbers</a>, and continue to divide the quotients until they can’t be separated anymore.</p>

13 <p>After factoring 49, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs</p>

14 <p>So, Prime factorization of 49 = 7 × 7 </p>

15 <p>But for 49, pairs of factor 7 are obtained.</p>

16 <p>So, it can be expressed as √49 = √(7 × 7) = 7</p>

17 <p> 7 is the simplest radical form of √49</p>

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20 <h3>Square Root of 49 By Long Division Method</h3>

19 <h3>Square Root of 49 By Long Division Method</h3>

21 <p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>

20 <p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>

22 <p>Follow the steps to calculate the square root of 49:</p>

21 <p>Follow the steps to calculate the square root of 49:</p>

23 <p><strong>Step 1:</strong>Write the number 49 and draw a bar above the pair of digits from right to left. 49 is a 2-digit number, so it is already a pair.</p>

22 <p><strong>Step 1:</strong>Write the number 49 and draw a bar above the pair of digits from right to left. 49 is a 2-digit number, so it is already a pair.</p>

24 <p><strong>Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 49. Here, it is 7 Because 72=49</p>

23 <p><strong>Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 49. Here, it is 7 Because 72=49</p>

25 <p><strong>Step 3:</strong>Now divide 49 by 7 (the number we got from Step 2) and we get a remainder of 0.</p>

24 <p><strong>Step 3:</strong>Now divide 49 by 7 (the number we got from Step 2) and we get a remainder of 0.</p>

26 <p> <strong>Step 4:</strong>The quotient obtained is the square root. In this case, it is 7.</p>

25 <p> <strong>Step 4:</strong>The quotient obtained is the square root. In this case, it is 7.</p>

27 <h3>Square Root of 49 By Subtraction Method</h3>

26 <h3>Square Root of 49 By Subtraction Method</h3>

28 <p>We know that the<a>sum</a>of the first n<a>odd numbers</a>is n2. We will use this fact to find square roots through the repeated<a>subtraction</a>method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:</p>

27 <p>We know that the<a>sum</a>of the first n<a>odd numbers</a>is n2. We will use this fact to find square roots through the repeated<a>subtraction</a>method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:</p>

29 <p><strong>Step 1:</strong>Take the number 49 and then subtract the first odd number from it. Here, in this case, it is 49-1=48</p>

28 <p><strong>Step 1:</strong>Take the number 49 and then subtract the first odd number from it. Here, in this case, it is 49-1=48</p>

30 <p><strong>Step 2:</strong>We have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 48, and again subtract the next odd number after 1, which is 3, → 48-3=45. Like this, we have to proceed further.</p>

29 <p><strong>Step 2:</strong>We have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 48, and again subtract the next odd number after 1, which is 3, → 48-3=45. Like this, we have to proceed further.</p>

31 <p><strong>Step 3</strong>: Now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 7 steps.</p>

30 <p><strong>Step 3</strong>: Now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 7 steps.</p>

32 <p>So, the square root is equal to the count, i.e., the square root of 49 is ±7.</p>

31 <p>So, the square root is equal to the count, i.e., the square root of 49 is ±7.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 49</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 49</h2>

34 <p>When we find the square root of 49, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions. </p>

33 <p>When we find the square root of 49, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions. </p>

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35 <h3>Problem 1</h3>

36 <p>Simplify √36 + √49+ √36 + √49 ?</p>

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

38 <p> √36 + √49 +√36 + √49</p>

39 <p>= 6 + 7 + 6 + 7</p>

40 <p>= 26</p>

41 <p>Answer : 26</p>

42 <h3>Explanation</h3>

43 <p> firstly, we found the values of the square roots of 36 and 49, then added the values. </p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>What is √49 multiplied by 7 and then subtracting 7 from it?</p>

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

48 <p> (√49 ⤬ 7) - 7</p>

49 <p>= (7⤬7)-7</p>

50 <p>= 49-7</p>

51 <p>=42</p>

52 <p>Answer: 42 </p>

53 <h3>Explanation</h3>

54 <p> breaking √49 into the simplest form , multiplying it by 7 and then subtracting 7 from the product . </p>

55 <p>Well explained 👍</p>

56 <h3>Problem 3</h3>

57 <p>Find the radius of a circle whose area is 49π cm².</p>

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

59 <p>Given, the area of the circle = 49π cm2</p>

60 <p>Now, area = πr2 (r is the radius of the circle)</p>

61 <p>So, πr2 = 49π cm2</p>

62 <p>We get, r2 = 49 cm2</p>

63 <p>r = √49 cm</p>

64 <p>Putting the value of √49 in the above equation, </p>

65 <p>We get, r = ±7 cm</p>

66 <p>Here we will consider the positive value of 7.</p>

67 <p>Therefore, the radius of the circle is 7 cm.</p>

68 <p>Answer: 7 cm. </p>

69 <h3>Explanation</h3>

70 <p>We know that, area of a circle = πr2 (r is the radius of the circle).According to this equation, we are getting the value of “r” as 7 cm by finding the value of the square root of 49. </p>

71 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

73 <p>In a right-angled triangle, the base is 24cm and the hypotenuse is 25cm. Find the measure of the height.</p>

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

75 <p>(base)2+(height)2=(hypotenuse)2</p>

76 <p>⇒ (height)2= (hypotenuse)2-(base)2</p>

77 <p>⇒ (height)2= 252-242</p>

78 <p>⇒(height)2=625-576</p>

79 <p>⇒(height)2=49</p>

80 <p>⇒height = √49</p>

81 <p>⇒ height= 7 </p>

82 <p>Answer: 7 cm </p>

83 <h3>Explanation</h3>

84 <p>According to Pythagoras Theorem, we find the measure of the height of the triangle using √49 </p>

85 <p>Well explained 👍</p>

86 <h3>Problem 5</h3>

87 <p>Find √49 / √7</p>

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

89 <p>√49/√7</p>

90 <p>= √(49/7)</p>

91 <p>=(√7 ╳ √7 )/√7</p>

92 <p>= √7</p>

93 <p>Answer : √7 ≅ 2.6457 </p>

94 <h3>Explanation</h3>

95 <p>we first broke √49 into √7 ╳ √7 and then divided the product by √7 . </p>

96 <p>Well explained 👍</p>

97 <h2>FAQs on 49 Square Root</h2>

98 <h3>1.What is the √49 in fraction?</h3>

99 <h3>2.What are the two square roots of 49?</h3>

100 <p>The two square roots of 49 are 7 and -7. </p>

101 <h3>3.Is 49 a perfect square or non-perfect square?</h3>

102 <p> 49 is a perfect square, since 49 =(7)2. </p>

103 <h3>4.Is the square root of 49 a rational or irrational number?</h3>

104 <p>The square root of 49 is ±7. So, 7 is a rational number, since it can be obtained by dividing two<a>integers</a>and can be written in the form p/q, where p and q are integers. </p>

105 <h3>5.Is √49 an integer?</h3>

106 <p>Yes, √49 =7 is an integer. </p>

107 <h2>Important Glossaries for Square Root of 49</h2>

108 <ul><li><strong>Exponential form: </strong>An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.Ex: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 or, 3 4 = 81, where 3 is the base, 4 is the exponent.</li>

109 </ul><ul><li><strong>Factorization: </strong>Expressing the given expression as a product of its factors Ex: 52=2 ⤬ 2 ⤬ 13 </li>

110 </ul><ul><li><strong>Prime Numbers:</strong>Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....</li>

111 </ul><ul><li><strong>Rational numbers and Irrational numbers:</strong>The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. </li>

112 </ul><ul><li><strong>perfect and non-perfect square numbers: </strong>Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :2, 8, 18</li>

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

114 <p>▶</p>

115 <h2>Jaskaran Singh Saluja</h2>

116 <h3>About the Author</h3>

117 <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>

118 <h3>Fun Fact</h3>

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