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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 various fields such as mathematics, engineering, and science. Here, we will discuss the square root of 985.</p>

4 <h2>What is the Square Root of 985?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 985 is not a<a>perfect square</a>. The square root of 985 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √985, whereas (985)^(1/2) in the exponential form. √985 ≈ 31.3847, 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 985</h2>

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

8 <h2>Square Root of 985 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 985 is broken down into its prime factors. Step 1: Finding the prime factors of 985. Breaking it down, we get 5 x 197. Since 985 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √985 using prime factorization is not feasible.</p>

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12 <h2>Square Root of 985 by Long Division Method</h2>

11 <h2>Square Root of 985 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 985, we need to group it as 85 and 9. Step 2: Now we need to find n whose square is close to 9. We can say n is '3' because 3 x 3 = 9, which is equal to 9. Now the<a>quotient</a>is 3, and after subtracting 9 from 9, the<a>remainder</a>is 0. Step 3: Now let us bring down 85, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor. Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 85. Let us consider n as 1, now 6 x 1 x 1 = 61. Step 5: Subtract 61 from 85; the difference is 24, and the quotient is 31. Step 6: Since the dividend is<a>less than</a>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 2400. Step 7: Now we need to find the new divisor, which is 618 because 618 x 3 = 1854. Step 8: Subtracting 1854 from 2400, we get the result 546. Step 9: The quotient now is 31.38. Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero. So the square root of √985 is approximately 31.38.</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 985, we need to group it as 85 and 9. Step 2: Now we need to find n whose square is close to 9. We can say n is '3' because 3 x 3 = 9, which is equal to 9. Now the<a>quotient</a>is 3, and after subtracting 9 from 9, the<a>remainder</a>is 0. Step 3: Now let us bring down 85, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor. Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 85. Let us consider n as 1, now 6 x 1 x 1 = 61. Step 5: Subtract 61 from 85; the difference is 24, and the quotient is 31. Step 6: Since the dividend is<a>less than</a>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 2400. Step 7: Now we need to find the new divisor, which is 618 because 618 x 3 = 1854. Step 8: Subtracting 1854 from 2400, we get the result 546. Step 9: The quotient now is 31.38. Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero. So the square root of √985 is approximately 31.38.</p>

14 <h2>Square Root of 985 by Approximation Method</h2>

13 <h2>Square Root of 985 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 985 using the approximation method. Step 1: Now we have to find the closest perfect squares of √985. The smallest perfect square less than 985 is 961, and the largest perfect square<a>greater than</a>985 is 1024. √985 falls somewhere between 31 and 32. Step 2: Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (985 - 961) / (1024 - 961) = 24/63 ≈ 0.38. 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 31 + 0.38 = 31.38, so the square root of 985 is approximately 31.38.</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 985 using the approximation method. Step 1: Now we have to find the closest perfect squares of √985. The smallest perfect square less than 985 is 961, and the largest perfect square<a>greater than</a>985 is 1024. √985 falls somewhere between 31 and 32. Step 2: Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (985 - 961) / (1024 - 961) = 24/63 ≈ 0.38. 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 31 + 0.38 = 31.38, so the square root of 985 is approximately 31.38.</p>

16 <h2>Common Mistakes and How to Avoid Them in the Square Root of 985</h2>

15 <h2>Common Mistakes and How to Avoid Them in the Square Root of 985</h2>

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

16 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping 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 √985?</p>

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

21 <p>The area of the square is 985 square units.</p>

22 <h3>Explanation</h3>

23 <p>The area of the square = side². The side length is given as √985. Area of the square = side² = √985 x √985 = 985. Therefore, the area of the square box is 985 square units.</p>

24 <p>Well explained 👍</p>

25 <h3>Problem 2</h3>

26 <p>A square-shaped building measuring 985 square feet is built; if each of the sides is √985, what will be the square feet of half of the building?</p>

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

28 <p>492.5 square feet</p>

29 <h3>Explanation</h3>

30 <p>We can just divide the given area by 2 as the building is square-shaped. Dividing 985 by 2 = we get 492.5. So half of the building measures 492.5 square feet.</p>

31 <p>Well explained 👍</p>

32 <h3>Problem 3</h3>

33 <p>Calculate √985 x 10.</p>

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

35 <p>313.847</p>

36 <h3>Explanation</h3>

37 <p>The first step is to find the square root of 985, which is approximately 31.3847. The second step is to multiply 31.3847 by 10. So, 31.3847 x 10 ≈ 313.847.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 4</h3>

40 <p>What will be the square root of (900 + 85)?</p>

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

42 <p>The square root is approximately 31.38.</p>

43 <h3>Explanation</h3>

44 <p>To find the square root, we need to find the sum of (900 + 85). 900 + 85 = 985, and then √985 ≈ 31.38. Therefore, the square root of (900 + 85) is approximately ±31.38.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 5</h3>

47 <p>Find the perimeter of the rectangle if its length ‘l’ is √985 units and the width ‘w’ is 40 units.</p>

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

49 <p>The perimeter of the rectangle is approximately 142.77 units.</p>

50 <h3>Explanation</h3>

51 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√985 + 40) = 2 × (31.3847 + 40) = 2 × 71.3847 ≈ 142.77 units.</p>

52 <p>Well explained 👍</p>

53 <h2>FAQ on Square Root of 985</h2>

54 <h3>1.What is √985 in its simplest form?</h3>

55 <p>The prime factorization of 985 is 5 x 197, so the simplest form of √985 remains √985, as it cannot be simplified further.</p>

56 <h3>2.Mention the factors of 985.</h3>

57 <p>Factors of 985 are 1, 5, 197, and 985.</p>

58 <h3>3.Calculate the square of 985.</h3>

59 <p>We get the square of 985 by multiplying the number by itself, that is 985 x 985 = 970225.</p>

60 <h3>4.Is 985 a prime number?</h3>

61 <h3>5.985 is divisible by?</h3>

62 <p>985 is divisible by 1, 5, 197, and 985.</p>

63 <h2>Important Glossaries for the Square Root of 985</h2>

64 <p>Square root: The square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4. Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. This is the reason it is also known as a principal square root. Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals. Long division method: A method used to find square roots of non-perfect squares through division, providing an approximate value.</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>