Square Root of 989
2026-02-28 08:34 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 989.

What is the Square Root of 989?

The square root is the inverse of the square of the number. 989 is not a perfect square. The square root of 989 is expressed in both radical and exponential form. In the radical form, it is expressed as √989, whereas (989)^(1/2) in the exponential form. √989 ≈ 31.446, 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 989

For perfect square numbers, the prime factorization method is often used. However, for non-perfect square numbers like 989, the long division method and approximation method are more suitable. Let us now learn the following methods: - Prime factorization method - Long division method - Approximation method

Square Root of 989 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 989 is broken down into its prime factors: Step 1: Finding the prime factors of 989 Breaking it down, we get 23 × 43: 23^1 × 43^1 Step 2: Now that we have found the prime factors of 989, the second step is to make pairs of those prime factors. Since 989 is not a perfect square, the digits of the number cannot be grouped into pairs. Therefore, calculating 989 using prime factorization yields no exact square root.

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Square Root of 989 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: Group the numbers from right to left. For 989, we group it as 89 and 9. Step 2: Find a number n whose square is less than or equal to 9. We can take n as 3 because 3 × 3 = 9. Now the quotient is 3, and after subtracting 9 - 9, the remainder is 0. Step 3: Bring down 89, which is the new dividend. Add the old divisor (3) with itself to get 6, which will be our new divisor. Step 4: Find a new n such that 6n × n ≤ 89. By checking, n=1 (61 × 1 = 61) fits the condition. Step 5: Subtract 61 from 89 to get the remainder 28, and the quotient is 31. Step 6: Add a decimal point, bring down 00 to make the new dividend 2800. Step 7: Now, find n such that 620n × n ≤ 2800. By trial, n=4 (620×4=2480) fits the condition. Step 8: Subtract 2480 from 2800 to get 320. Step 9: The quotient is 31.4. Continue the steps until you reach the desired precision. So the square root of √989 is approximately 31.446.

Square Root of 989 by Approximation Method

The approximation method is another method for finding square roots and provides a straightforward way to estimate the square root of a given number. Let's see how to find the square root of 989 using this method. Step 1: Find the closest perfect squares of √989. The closest perfect squares are 961 (31^2) and 1024 (32^2). Thus, √989 falls between 31 and 32. Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using the formula: (989 - 961) / (1024 - 961) = 28 / 63 ≈ 0.444 Adding the value to the lower bound, we get 31 + 0.444 = 31.444, so the square root of 989 is approximately 31.444.

Common Mistakes and How to Avoid Them in the Square Root of 989

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at some common mistakes in detail.

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Problem 1

If the side length of a square box is given as √989, what is its area?

Okay, lets begin

The area of the square is approximately 989 square units.

Explanation

The area of the square = side^2. The side length is given as √989. Area of the square = side^2 = √989 × √989 = 989.

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Problem 2

A square-shaped building measures 989 square feet; if each side is √989, what will be the square feet of half of the building?

Okay, lets begin

494.5 square feet

Explanation

To find half the area, divide the given area by 2. 989 / 2 = 494.5 square feet.

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Problem 3

Calculate √989 × 5.

Okay, lets begin

Approximately 157.23

Explanation

First, find the square root of 989, which is approximately 31.446. Then multiply 31.446 by 5. 31.446 × 5 ≈ 157.23.

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Problem 4

What will be the square root of (989 + 11)?

Okay, lets begin

The square root is 32.

Explanation

First, find the sum of (989 + 11) = 1000. The square root of 1000 is approximately 31.622.

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Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √989 units and the width ‘w’ is 40 units.

Okay, lets begin

Approximately 142.892 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√989 + 40) = 2 × (31.446 + 40) = 2 × 71.446 = 142.892 units.

Well explained 👍

FAQ on Square Root of 989

1.What is √989 in its simplest form?

The prime factorization of 989 is 23 × 43. Since these are distinct primes, √989 cannot be simplified further.

2.Mention the factors of 989.

Factors of 989 are 1, 23, 43, and 989.

3.Calculate the square of 989.

We get the square of 989 by multiplying the number by itself: 989 × 989 = 978121.

4.Is 989 a prime number?

5.989 is divisible by?

989 is divisible by 1, 23, 43, and 989.

Important Glossaries for the Square Root of 989

Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, so √16 = 4. Irrational number: An irrational number 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, the positive square root is typically used due to its common applications in the real world. This is known as the principal square root. Prime Factorization: Prime factorization is expressing a number as the product of its prime factors. Long Division Method: A method used to find the square root of a number by dividing it into groups of digits from right to left and using a series of steps to find the root.

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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.