122 LearnersLast updated on May 26th, 2025
Square Root of 1089
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 1089.
What is the Square Root of 1089?
The square root is the inverse of the square of a number. 1089 is a perfect square. The square root of 1089 is expressed in both radical and exponential form. In radical form, it is expressed as √1089, whereas (1089)^(1/2) in exponential form. √1089 = 33, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1089
The prime factorization method is used for perfect square numbers. However, the long-division method and approximation method can also be used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1089 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1089 is broken down into its prime factors.
Step 1: Finding the prime factors of 1089 Breaking it down, we get 3 x 3 x 11 x 11: 3^2 x 11^2
Step 2: Now we found out the prime factors of 1089. The second step is to make pairs of those prime factors. Since 1089 is a perfect square, we can pair the digits.
Therefore, the square root of 1089 using prime factorization is 3 x 11 = 33.
Square Root of 1089 by Long Division Method
The long division method can be used for 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 1089, we need to group it as 89 and 10.
Step 2: Now we need to find n whose square is closest to 10. We can say n as '3' because 3 x 3 = 9, which is lesser than or equal to 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.
Step 3: Now let us bring down 89, which is the new dividend. Add the old divisor with the same number 3 + 3, and we get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 189. Let us consider n as 3, now 6 x 3 x 3 = 189.
Step 6: Subtract 189 from 189, and the difference is 0, and the quotient is 33.
Step 7: Since we have no remainder, the square root of 1089 is exactly 33.
Square Root of 1089 by Approximation Method
Approximation method is another method for finding the square roots, and 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 1089 using the approximation method.
Step 1: Now we have to find the closest perfect square to √1089. The closest perfect square of 1089 is 1024 and 1156. √1089 falls exactly on 33.
Step 2: Since 1089 is a perfect square, the square root is exactly 33.
Common Mistakes and How to Avoid Them in the Square Root of 1089
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √121 = 11, there is also -11, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(16+25) = √16 + √25 is a wrong method of using roots. The right way of using roots is √(16+25) = √41.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example: √64 and ∛64 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1089 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1089?
The area of the square is 1089 square units.
Explanation
The area of the square = side².
The side length is given as √1089.
Area of the square = side²
= √1089 x √1089
= 33 x 33
= 1089.
Therefore, the area of the square box is 1089 square units.
Problem 2
A square-shaped building measuring 1089 square feet is built; if each of the sides is √1089, what will be the square feet of half of the building?
544.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1089 by 2, we get 544.5.
So half of the building measures 544.5 square feet.
Problem 3
Calculate √1089 x 5.
165
Explanation
The first step is to find the square root of 1089, which is 33.
The second step is to multiply 33 with 5.
So 33 x 5 = 165.
Problem 4
What will be the square root of (1089 + 11)?
The square root is 33.17
Explanation
To find the square root, we need to find the sum of (1089 + 11). 1089 + 11 = 1100, and then √1100 ≈ 33.17.
Therefore, the square root of (1089 + 11) is approximately ±33.17.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1089 units and the width 'w' is 22 units.
We find the perimeter of the rectangle as 110 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1089 + 22)
= 2 × (33 + 22)
= 2 × 55
= 110 units.
FAQ on Square Root of 1089
1.What is √1089 in its simplest form?
2.Mention the factors of 1089.
3.Calculate the square of 1089.
4.Is 1089 a prime number?
5.1089 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 1089?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 1089?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 1089
- Square root: A square root is the inverse of a square. Example: 6² = 36, and the inverse of the square is the square root, that is, √36 = 6.
- Rational number: A rational number is a number that can be written in the form p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A number that is the square of an integer. For example, 1089 is a perfect square because it is 33².
- Divisor: A divisor is a number that divides another number completely without leaving a remainder.
- Integer: An integer is a whole number that can be positive, negative, or zero. Examples: -3, 0, 7.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
