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

3 <p>The square root of 2 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 2. The number 2 has a unique non-negative square root, called the principal square root.</p>

4 <h2>What Is the Square Root of 2?</h2>

5 <p>The<a>square</a>root of 2 is ±1.41421356237, where is 1.41421356237 the positive solution of the<a>equation</a>x2 = 2. </p>

6 <p>Finding the square root is just the inverse of squaring a<a>number</a>and hence, squaring 1.41421356237 will result in 2.</p>

7 <p>The square root of 2 is written as √2 in radical form, where the ‘√’ sign is called the “radical” sign. In<a>exponential form</a>, it is written as (2)1/2 .</p>

8 <h2>Finding the Square Root of 2</h2>

9 <p>We can find the<a>square root</a>of 2 through various methods. They are: i) Prime factorization method ii) Long<a>division</a>method iii) Approximation/Estimation method </p>

10 <h3>Square Root of 2 By Prime Factorization Method</h3>

11 <p>The<a>prime factorization</a>of 2 is done by dividing 2 by<a>prime numbers</a>and continuing to divide the quotients until they can’t be separated anymore.</p>

12 <p>After factorizing 2, make pairs out of the<a>factors</a>to get the square root. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs.</p>

13 <p>So, Prime factorization of 2 = 2 × 1 But here in the case of 2, no pairs of factors can be obtained but a single 2 is remaining</p>

14 <p>So, it can be expressed as √2 √2 is the simplest radical form.</p>

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17 <h3>Square Root of 2 By Long Division Method</h3>

16 <h3>Square Root of 2 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 2:</p>

18 <p>Follow the steps to calculate the square root of 2:</p>

20 <p> Step 1: Write the number 2, and draw a bar above the pair of digits from right to left.</p>

19 <p> Step 1: Write the number 2, and draw a bar above the pair of digits from right to left.</p>

21 <p> Step 2: Now, find the greatest number whose square is<a>less than</a>or equal to. Here, it is 1, Because 12=1 < 2.</p>

20 <p> Step 2: Now, find the greatest number whose square is<a>less than</a>or equal to. Here, it is 1, Because 12=1 < 2.</p>

22 <p>Step 3 : Now divide 2 by 1 (the number we got from Step 2) such that we get 1 as quotient and we get a remainder. </p>

21 <p>Step 3 : Now divide 2 by 1 (the number we got from Step 2) such that we get 1 as quotient and we get a remainder. </p>

23 <p>Double the divisor 1, we get 2, and then the largest possible number A1=4 is chosen such that when 4 is written beside the new divisor, 2, a 2-digit number is formed →24, and multiplying 4 with 24 gives 96 which is less than 100.</p>

22 <p>Double the divisor 1, we get 2, and then the largest possible number A1=4 is chosen such that when 4 is written beside the new divisor, 2, a 2-digit number is formed →24, and multiplying 4 with 24 gives 96 which is less than 100.</p>

24 <p> Repeat the process until you reach the remainder of 0. We are left with the remainder, 3836 (refer to the picture), after some iterations and keeping the division till here, at this point.</p>

23 <p> Repeat the process until you reach the remainder of 0. We are left with the remainder, 3836 (refer to the picture), after some iterations and keeping the division till here, at this point.</p>

25 <p> Step 4 : The quotient obtained is the square root. In this case, it is 1.4142….</p>

24 <p> Step 4 : The quotient obtained is the square root. In this case, it is 1.4142….</p>

26 <p></p>

25 <p></p>

27 <h3>Square Root of 2 By Approximation</h3>

26 <h3>Square Root of 2 By Approximation</h3>

28 <p>Approximation or<a>estimation</a>of the square root is not the exact square root, but it is an estimate.</p>

27 <p>Approximation or<a>estimation</a>of the square root is not the exact square root, but it is an estimate.</p>

29 <p>Here, through this method, an approximate value of square root is found by guessing.</p>

28 <p>Here, through this method, an approximate value of square root is found by guessing.</p>

30 <p>Follow the steps below:</p>

29 <p>Follow the steps below:</p>

31 <p>Step 1: identify the square roots of the perfect squares above and below 2 Below : 1→ square root of 1 = 1 ……..(i) Above : 4 →square root of 4 = 2 ……..(ii)</p>

30 <p>Step 1: identify the square roots of the perfect squares above and below 2 Below : 1→ square root of 1 = 1 ……..(i) Above : 4 →square root of 4 = 2 ……..(ii)</p>

32 <p>Step 2: Dividing 2 with one of 1 or 2 If we choose 1 We get 2 when 2 is divided by 1 …….(iii)</p>

31 <p>Step 2: Dividing 2 with one of 1 or 2 If we choose 1 We get 2 when 2 is divided by 1 …….(iii)</p>

33 <p> Step 3: Find the<a>average</a>of 1 (from (i)) and 2 (from (iii)) (1+2)/2 = 1.5 </p>

32 <p> Step 3: Find the<a>average</a>of 1 (from (i)) and 2 (from (iii)) (1+2)/2 = 1.5 </p>

34 <p> Hence, 1.5 is the approximate square root of 2</p>

33 <p> Hence, 1.5 is the approximate square root of 2</p>

35 <h2>Common Mistakes and How to Avoid Them in the Square Root of 2</h2>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 2</h2>

36 <p>When we find the square root of 2, 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>

35 <p>When we find the square root of 2, 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>

36 + <h2>Download Worksheets</h2>

37 <h3>Problem 1</h3>

38 <p>Find the value of 1/√2 in rationalized form.</p>

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

40 <p>1/√2 ⤫ √2/ √2 = √2/2 Answer: √2/2</p>

41 <h3>Explanation</h3>

42 <p>Rationalizing 1/√2 and getting the result.</p>

43 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

45 <p>Find the length of a side of a square whose area is 2 cm².</p>

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

47 <p>Given, the area = 2 cm2 We know that, (side of a square)2 = area of square Or, (side of a square)2 = 2 Or, (side of a square)= √2 Or, the side of a square = 1.4142 But, length of a square is a positive quantity only, so, length of the side is 1.4142 cm. Answer: 1.4142 cm </p>

48 <h3>Explanation</h3>

49 <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>

50 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

52 <p>Simplify (√2 + √2) ⤫ √2.</p>

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

54 <p> (√2 + √2) ⤫ √2 = (1.4142 + 1.4142) ⤫ 1.4142 = 2.8284 ⤫ 1.4142 = 3.9999 Answer: 3.9999 </p>

55 <h3>Explanation</h3>

56 <p>We first solved the part inside the brackets, i.e., √2 + √2, which resulted into 2.8284 and then multiplying it with √2 which is 1.4142 we get 3.9999.</p>

57 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

59 <p>If y=√2, find y²</p>

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

61 <p>Firstly, y=√2= 1.4142 Now, squaring y, we get, y2= (1.4142)2=2 or, y2=2 Answer : 2 </p>

62 <h3>Explanation</h3>

63 <p>Squaring “y” which is same as squaring the value of √2 resulted to 2.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

66 <p>Calculate (√2/2 + √2/4)</p>

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

68 <p>√2/2 + √2/4 = 1.4142/ 2 + 1.4142/4 = 0.7071 + 0.35355 = 1.06065 Answer : 1.06065 </p>

69 <h3>Explanation</h3>

70 <p>From the given expression, we first found the value of square root of 2 then solved by simple divisions and then simple addition.</p>

71 <p>Well explained 👍</p>

72 <h2>FAQs on 2 Square Root</h2>

73 <h3>1.What is the exact value of the square root of 2 in terms of radicals?</h3>

74 <p>The exact value is expressed as √2. </p>

75 <h3>2.Is the square root of 2 a whole number?</h3>

76 <p>No, 1.41421356237 the square root of 2, is not a<a>whole number</a>.</p>

77 <h3>3.Is 2 a perfect square or a non-perfect square?</h3>

78 <p>2 is a non-perfect square, since 2 =(1.41421356237)2.</p>

79 <h3>4.Is the square root of 2 a rational or irrational number?</h3>

80 <p>The square root of 2 is ±1.41421356237. So, 1.41421356237is an<a>irrational number</a>, since it cannot be obtained by dividing two<a>integers</a>and cannot be written in the form p/q, where p and q are integers.</p>

81 <h3>5.What is the principal square root of 2?</h3>

82 <p>The principal square root of 2 is ±1.41421356237, the positive value, but not -1.41421356237. </p>

83 <h3>6.Is the square root of 2 a real number ?</h3>

84 <h2>Important Glossaries for Square Root of 2</h2>

85 <p>1)Exponential form</p>

86 <p>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>

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

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

89 <p>4) Rational numbers and Irrational numbers</p>

90 <p>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>

91 <p>5) Perfect and non-perfect square numbers 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>

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

93 <p>▶</p>

94 <h2>Jaskaran Singh Saluja</h2>

95 <h3>About the Author</h3>

96 <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>

97 <h3>Fun Fact</h3>

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