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

3 <p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 744.</p>

4 <h2>What is the Square Root of 744?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 744 is not a<a>perfect square</a>. The square root of 744 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √744, whereas in exponential form it is expressed as (744)^(1/2). √744 ≈ 27.284, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

6 <h2>Finding the Square Root of 744</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not typically used for non-perfect square numbers, where the long-<a>division</a>method and approximation method are more suitable. Let us now learn about the following methods: - Prime factorization method - Long division method - Approximation method</p>

8 <h2>Square Root of 744 by Prime Factorization Method</h2>

9 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 744 is broken down into its prime factors: Step 1: Finding the prime factors of 744 Breaking it down, we get 2 × 2 × 2 × 3 × 31: 2^3 × 3 × 31 Step 2: Now we have found the prime factors of 744. The second step is to make pairs of those prime factors. Since 744 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √744 using prime factorization is not straightforward.</p>

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12 <h2>Square Root of 744 by Long Division Method</h2>

11 <h2>Square Root of 744 by Long Division Method</h2>

13 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step: Step 1: To begin with, we need to group the numbers from right to left. In the case of 744, we need to group it as 44 and 7. Step 2: Now we need to find n whose square is<a>less than</a>or equal to 7. We can say n is ‘2’ because 2 × 2 = 4 is lesser than or equal to 7. Now the<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3. Step 3: Now let us bring down 44, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 2 + 2, we get 4, which will be our new divisor. Step 4: The new divisor will be 4n. We need to find the value of n such that 4n × n is less than or equal to 344. Step 5: The next step is finding 4n × n ≤ 344. Let us consider n as 7, now 47 × 7 = 329. Step 6: Subtract 344 from 329; the difference is 15, and the quotient is 27. Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1500. Step 8: Now we need to find the new divisor, which is 547 because 547 × 2 = 1094. Step 9: Subtracting 1094 from 1500, we get 406. Step 10: Now, the quotient is 27.2. Step 11: Continue doing these steps until we get two decimal places. If there is no decimal value, continue until the remainder is zero. So the square root of √744 is approximately 27.28.</p>

12 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step: Step 1: To begin with, we need to group the numbers from right to left. In the case of 744, we need to group it as 44 and 7. Step 2: Now we need to find n whose square is<a>less than</a>or equal to 7. We can say n is ‘2’ because 2 × 2 = 4 is lesser than or equal to 7. Now the<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3. Step 3: Now let us bring down 44, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 2 + 2, we get 4, which will be our new divisor. Step 4: The new divisor will be 4n. We need to find the value of n such that 4n × n is less than or equal to 344. Step 5: The next step is finding 4n × n ≤ 344. Let us consider n as 7, now 47 × 7 = 329. Step 6: Subtract 344 from 329; the difference is 15, and the quotient is 27. Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1500. Step 8: Now we need to find the new divisor, which is 547 because 547 × 2 = 1094. Step 9: Subtracting 1094 from 1500, we get 406. Step 10: Now, the quotient is 27.2. Step 11: Continue doing these steps until we get two decimal places. If there is no decimal value, continue until the remainder is zero. So the square root of √744 is approximately 27.28.</p>

14 <h2>Square Root of 744 by Approximation Method</h2>

13 <h2>Square Root of 744 by Approximation Method</h2>

15 <p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 744 using the approximation method. Step 1: Now we have to find the closest perfect squares of √744. The smallest perfect square below 744 is 729 (27^2) and the next largest perfect square is 784 (28^2). √744 falls somewhere between 27 and 28. Step 2: Now we need to apply the<a>formula</a>that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (744 - 729) / (784 - 729) = 15 / 55 ≈ 0.273. Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number which is 27 + 0.273 ≈ 27.273, so the square root of 744 is approximately 27.28.</p>

14 <p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 744 using the approximation method. Step 1: Now we have to find the closest perfect squares of √744. The smallest perfect square below 744 is 729 (27^2) and the next largest perfect square is 784 (28^2). √744 falls somewhere between 27 and 28. Step 2: Now we need to apply the<a>formula</a>that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (744 - 729) / (784 - 729) = 15 / 55 ≈ 0.273. Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number which is 27 + 0.273 ≈ 27.273, so the square root of 744 is approximately 27.28.</p>

16 <h2>Common Mistakes and How to Avoid Them in the Square Root of 744</h2>

15 <h2>Common Mistakes and How to Avoid Them in the Square Root of 744</h2>

17 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, or skipping steps in long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

16 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, or skipping steps in long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

17 + <h2>Download Worksheets</h2>

18 <h3>Problem 1</h3>

19 <p>Can you help Max find the area of a square box if its side length is given as √744?</p>

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

21 <p>The area of the square is approximately 554.06 square units.</p>

22 <h3>Explanation</h3>

23 <p>The area of the square = side^2. The side length is given as √744. Area of the square = side^2 = √744 × √744 ≈ 27.28 × 27.28 ≈ 744. Therefore, the area of the square box is approximately 744 square units.</p>

24 <p>Well explained 👍</p>

25 <h3>Problem 2</h3>

26 <p>A square-shaped plot measuring 744 square feet is designed; if each of the sides is √744, what will be the square feet of half of the plot?</p>

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

28 <p>372 square feet</p>

29 <h3>Explanation</h3>

30 <p>We can just divide the given area by 2 as the plot is square-shaped. Dividing 744 by 2, we get 372. So half of the plot measures 372 square feet.</p>

31 <p>Well explained 👍</p>

32 <h3>Problem 3</h3>

33 <p>Calculate √744 × 5.</p>

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

35 <p>Approximately 136.42</p>

36 <h3>Explanation</h3>

37 <p>The first step is to find the square root of 744, which is approximately 27.28. The second step is to multiply 27.28 by 5. So, 27.28 × 5 ≈ 136.42.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 4</h3>

40 <p>What will be the square root of (744 + 16)?</p>

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

42 <p>The square root is 28.</p>

43 <h3>Explanation</h3>

44 <p>To find the square root, we need to find the sum of (744 + 16). 744 + 16 = 760, and then √760 ≈ 27.57. Therefore, the square root of (744 + 16) is approximately ±27.57.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 5</h3>

47 <p>Find the perimeter of the rectangle if its length ‘l’ is √744 units and the width ‘w’ is 38 units.</p>

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

49 <p>The perimeter of the rectangle is approximately 130.56 units.</p>

50 <h3>Explanation</h3>

51 <p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√744 + 38) = 2 × (27.28 + 38) = 2 × 65.28 = 130.56 units.</p>

52 <p>Well explained 👍</p>

53 <h2>FAQ on Square Root of 744</h2>

54 <h3>1.What is √744 in its simplest form?</h3>

55 <p>The prime factorization of 744 is 2 × 2 × 2 × 3 × 31, so the simplest form of √744 is √(2^3 × 3 × 31).</p>

56 <h3>2.Mention the factors of 744.</h3>

57 <p>Factors of 744 are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, and 744.</p>

58 <h3>3.Calculate the square of 744.</h3>

59 <p>We get the square of 744 by multiplying the number by itself, that is 744 × 744 = 553536.</p>

60 <h3>4.Is 744 a prime number?</h3>

61 <h3>5.744 is divisible by?</h3>

62 <p>744 has many factors; those are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, and 744.</p>

63 <h2>Important Glossaries for the Square Root of 744</h2>

64 <p>Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4. Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers, where the denominator is not zero. Approximation method: A method of finding an approximate value of a number, often used when calculating the square root of non-perfect squares. Decimal: A number that consists of a whole number and a fractional part separated by a decimal point, for example, 7.86, 8.65, and 9.42. Long Division Method: A step-by-step division process used to find the square root of numbers that are not perfect squares.</p>

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

66 <p>▶</p>

67 <h2>Jaskaran Singh Saluja</h2>

68 <h3>About the Author</h3>

69 <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>

70 <h3>Fun Fact</h3>

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