Last updated on May 26th, 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 fields such as vehicle design, finance, etc. Here, we will discuss 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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √1089 x 5.
165
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.
What will be the square root of (1089 + 11)?
The square root is 33.17
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1089 + 22)
= 2 × (33 + 22)
= 2 × 55
= 110 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.