Square Root of 985
2026-02-28 09:16 Diff
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Last updated on August 5, 2025

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.

What is the Square Root of 985?

The square root is the inverse of the square of the number. 985 is not a perfect square. The square root of 985 is expressed in both radical and exponential form. In the radical form, it is expressed as √985, whereas (985)^(1/2) in the exponential form. √985 ≈ 31.3847, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 985

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

Square Root of 985 by Prime Factorization Method

The product of prime factors 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.

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Square Root of 985 by Long Division Method

The long division 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 square root 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 quotient is 3, and after subtracting 9 from 9, the remainder is 0. Step 3: Now let us bring down 85, which is the new dividend. Add the old divisor 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 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 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.

Square Root of 985 by Approximation Method

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 greater than 985 is 1024. √985 falls somewhere between 31 and 32. Step 2: Now we need to apply the formula: (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 decimal 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.

Common Mistakes and How to Avoid Them in the Square Root of 985

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.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √985?

Okay, lets begin

The area of the square is 985 square units.

Explanation

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.

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Problem 2

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?

Okay, lets begin

492.5 square feet

Explanation

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.

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Problem 3

Calculate √985 x 10.

Okay, lets begin

313.847

Explanation

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.

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Problem 4

What will be the square root of (900 + 85)?

Okay, lets begin

The square root is approximately 31.38.

Explanation

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.

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Problem 5

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

Okay, lets begin

The perimeter of the rectangle is approximately 142.77 units.

Explanation

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

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FAQ on Square Root of 985

1.What is √985 in its simplest form?

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

2.Mention the factors of 985.

Factors of 985 are 1, 5, 197, and 985.

3.Calculate the square of 985.

We get the square of 985 by multiplying the number by itself, that is 985 x 985 = 970225.

4.Is 985 a prime number?

5.985 is divisible by?

985 is divisible by 1, 5, 197, and 985.

Important Glossaries for the Square Root of 985

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.

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Jaskaran Singh Saluja

About the Author

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.

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: He loves to play the quiz with kids through algebra to make kids love it.