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

3 <p>The square root of 4 is a value “y” such that when “y” is multiplied by itself → y × y, the result is 4. The number 4 has a unique non-negative square root, called the principal square root.</p>

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

5 <p>The<a>square</a>root<a>of</a>4 is ±2, where 2 is the positive solution of the<a>equation</a> x2 = 4. Finding the square root is just the inverse of squaring a<a>number</a>and hence, squaring 2 will result in 4. The square root of 4 is written as √4 in radical form, where the ‘√’ sign is called the “radical” sign. In<a>exponential form</a>, it is written as (4)1/2 </p>

6 <h3>Finding the Square Root of 4</h3>

7 <p>We can find the<a>square root</a>of 4 through various methods. They are:</p>

8 <p><a>i</a>) Prime factorization method</p>

9 <p>ii) Long<a>division</a>method</p>

10 <p>iii) Repeated<a>subtraction</a>method </p>

11 <h3>Square Root of 4 By Prime Factorization Method</h3>

12 <p>The<a>prime factorization</a>of 4 can be found by dividing the number by<a>prime numbers</a>and continuing to divide the quotients until they can’t be separated anymore. We first prime factorize 4 and then make pairs of two to get the square root.</p>

13 <p>So, Prime factorization of 4 = 2 ×2 </p>

14 <p>Square root of 4= √[2 × 2] = 2 </p>

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17 <h3>Square Root of 4 By Long Division Method</h3>

16 <h3>Square Root of 4 By Long Division Method</h3>

18 <p>This method is 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>

17 <p>This method is 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>

19 <p>Follow the steps to calculate the square root of 4.</p>

18 <p>Follow the steps to calculate the square root of 4.</p>

20 <p><strong> Step 1:</strong>Write the number 4 and draw a bar above the pair of digits from right to left.</p>

19 <p><strong> Step 1:</strong>Write the number 4 and draw a bar above the pair of digits from right to left.</p>

21 <p><strong> Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 4. Here, it is</p>

20 <p><strong> Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 4. Here, it is</p>

22 <p>2 because 22=4 </p>

21 <p>2 because 22=4 </p>

23 <p><strong>Step 3:</strong>now divide 4 by 2 (the number we got from Step 2) such that we get 2 as a quotient, and we get a remainder 0. </p>

22 <p><strong>Step 3:</strong>now divide 4 by 2 (the number we got from Step 2) such that we get 2 as a quotient, and we get a remainder 0. </p>

24 <p> <strong>Step 4:</strong>The quotient obtained is the square root of 4. In this case, it is 2.</p>

23 <p> <strong>Step 4:</strong>The quotient obtained is the square root of 4. In this case, it is 2.</p>

25 <h3>Square Root of 4 By Subtraction Method</h3>

24 <h3>Square Root of 4 By Subtraction Method</h3>

26 <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 subtraction 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>

25 <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 subtraction 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><strong>Step 1:</strong>take the number 4 and then subtract the first odd number from it. Here, in this case, it is 4-1=3</p>

26 <p><strong>Step 1:</strong>take the number 4 and then subtract the first odd number from it. Here, in this case, it is 4-1=3</p>

28 <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., 3, and again subtract the next odd number after 1, which is 3, → 3-3=0.</p>

27 <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., 3, and again subtract the next odd number after 1, which is 3, → 3-3=0.</p>

29 <p><strong>Step 3:</strong>Now we have to count the number of subtraction steps it takes to yield 0 finally. </p>

28 <p><strong>Step 3:</strong>Now we have to count the number of subtraction steps it takes to yield 0 finally. </p>

30 <p>Here, in this case, it takes 2 steps So, the square root is equal to the count, i.e., the square root of 4 is ±2.</p>

29 <p>Here, in this case, it takes 2 steps So, the square root is equal to the count, i.e., the square root of 4 is ±2.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4</h2>

32 <p>When we find the square root of 4, 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>

31 <p>When we find the square root of 4, 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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33 <h3>Problem 1</h3>

34 <p>Find √(4×9) ?</p>

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

36 <p>√4 × 20/5</p>

37 <p>= 2×4</p>

38 <p>= 8</p>

39 <p>Answer: 8 </p>

40 <h3>Explanation</h3>

41 <p>finding the value of √4 and multiplying by 20/5. </p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>Find the radius of a circle whose area is 4π cm².</p>

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

46 <p>Given, the area of the circle = 4π cm2</p>

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

48 <p>So, πr2 = 4π cm2</p>

49 <p>We get, r2 = 4 cm2</p>

50 <p> r = √4 cm</p>

51 <p>Putting the value of √4 in the above equation,</p>

52 <p>We get, r = ±2 cm</p>

53 <p>Here we will consider the positive value of 2</p>

54 <p>Therefore, the radius of the circle is 2 cm.</p>

55 <p>Answer: 2 cm. </p>

56 <h3>Explanation</h3>

57 <p>We know that, area of a circle = πr2 (r is the radius of the circle)</p>

58 <p>According to this equation, we are getting the value of “r” as 2 cm by finding the value of the square root of 4</p>

59 <p>Well explained 👍</p>

60 <h3>Problem 3</h3>

61 <p>Find the length of a side of a square whose area is 4 cm²</p>

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

63 <p>Given, the area = 4 cm2</p>

64 <p>We know that, (side of a square)2 = area of square</p>

65 <p>Or, (side of a square)2 = 4</p>

66 <p>Or, (side of a square)= √4</p>

67 <p> Or, the side of a square = ± 2.</p>

68 <p>But, the length of a square is a positive quantity only, so, the length of the side is 2 cm.</p>

69 <p>Answer: 2 cm </p>

70 <h3>Explanation</h3>

71 <p>We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square </p>

72 <p>Well explained 👍</p>

73 <h3>Problem 4</h3>

74 <p>Find (√4 / √49) × (√36/√64)</p>

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

76 <p>(√4 / √49) × (√36/√64)</p>

77 <p>=(2/7)×(6/8) </p>

78 <p>= 3/14 </p>

79 <h3>Explanation</h3>

80 <p>we firstly found out the values of √4, √49,√36 and √64 then solved .</p>

81 <p>Well explained 👍</p>

82 <h2>FAQs on 4 Square Root</h2>

83 <h3>1.What are the factors of 4 ?</h3>

84 <p> Factors of 4 are the numbers which divide 4 exactly, leaving no remainder. Those are 1,2, and 4. </p>

85 <h3>2.What is the cube root of 4?</h3>

86 <p>The<a>cube</a>root of 4 is found through Halley's method, and hence we get an approximate value of 1.5874… . </p>

87 <h3>3.Is 4 a perfect square or non-perfect square?</h3>

88 <p> 4 is a perfect square, since it is the square of a whole<a>rational number</a>2, and it is 4= (2) 2. </p>

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

90 <p>The square root of 4 is ±2. So, 2 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>

91 <h3>5.How to solve √10?</h3>

92 <p>√10 can be solved through various methods like Long Division Method, Prime Factorization method or Approximation method. The value is 3.16227766017. </p>

93 <h2>Important Glossaries for Square Root of 4</h2>

94 <p><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: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent </p>

95 <p><strong>Factorization</strong> - Expressing the given expression as a product of its factors Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3</p>

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

97 <p><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. </p>

98 <p><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 :3, 8, 24 </p>

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

100 <p>▶</p>

101 <h2>Jaskaran Singh Saluja</h2>

102 <h3>About the Author</h3>

103 <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>

104 <h3>Fun Fact</h3>

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