128 LearnersLast updated on May 26th, 2025
Square Root of 1083
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 engineering, finance, etc. Here, we will discuss the square root of 1083.
What is the Square Root of 1083?
The square root is the inverse of the square of the number. 1083 is not a perfect square. The square root of 1083 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1083, whereas (1083)^(1/2) in the exponential form. √1083 ≈ 32.89377, 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 1083
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 1083 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1083 is broken down into its prime factors:
Step 1: Finding the prime factors of 1083 Breaking it down, we get 3 x 3 x 3 x 3 x 13 = 3^4 x 13
Step 2: Now we found out the prime factors of 1083. The next step is to make pairs of those prime factors. Since 1083 is not a perfect square, the digits of the number can’t be grouped in pairs completely.
Therefore, calculating 1083 using prime factorization is not straightforward.
Square Root of 1083 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 1083, we need to group it as 83 and 10.
Step 2: Now we need to find n whose square is ≤ 10. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.
Step 3: Now let us bring down 83, making the new dividend 183. Add the previous divisor (3) with the same number to get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the previous divisor and quotient. Now we use 6n as the new divisor and need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 183. Let us consider n as 3; now, 63 × 3 = 189, which is too large. Trying n as 2, we get 62 × 2 = 124.
Step 6: Subtract 124 from 183; the difference is 59, and the quotient is 32.
Step 7: 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 5900.
Step 8: Find the new divisor, which is 649, because 649 × 9 = 5841. Step 9: Subtracting 5841 from 5900, we get the result 59.
Step 10: Now the quotient is 32.9.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √1083 is approximately 32.89.
Square Root of 1083 by Approximation Method
The 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 1083 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1083. The smallest perfect square less than 1083 is 1024, and the largest perfect square greater than 1083 is 1089. √1083 falls somewhere between 32 and 33.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (1083 - 1024) ÷ (1089 - 1024) = 59 / 65 = 0.9077. 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 32 + 0.91 = 32.91.
So the square root of 1083 is approximately 32.91.
Common Mistakes and How to Avoid Them in the Square Root of 1083
Students do make mistakes while finding the square root, such as forgetting the negative square root and skipping steps in the long division method. 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 has both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one.
For example, √50 = 7.071, but there is also -7.071 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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to the next step.
For example, √(12+24) = √12 + √24 is an incorrect method of using roots. The correct way is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students 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 incorrect; 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 roots and square roots, as this will help them avoid mistakes.
For example, √50 and ∛50 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 problem. This may occur during subtraction or other steps.
Square Root of 1083 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1083?
The area of the square is approximately 1173.23 square units.
Explanation
The area of the square = side².
The side length is given as √1083.
Area of the square = side²
= √1083 × √1083
≈ 32.89 × 32.89
≈ 1083.
Therefore, the area of the square box is approximately 1083 square units.
Problem 2
A square-shaped building measuring 1083 square feet is built; if each of the sides is √1083, what will be the square feet of half of the building?
541.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1083 by 2, we get 541.5.
So half of the building measures 541.5 square feet.
Problem 3
Calculate √1083 × 5.
164.465
Explanation
The first step is to find the square root of 1083, which is approximately 32.89.
The second step is to multiply 32.89 by 5.
So, 32.89 × 5 = 164.465.
Problem 4
What will be the square root of (1024 + 59)?
The square root is approximately 32.89.
Explanation
To find the square root, we need to find the sum of (1024 + 59).
1024 + 59 = 1083, and then √1083 ≈ 32.89.
Therefore, the square root of (1024 + 59) is approximately ±32.89.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1083 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 141.78 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1083 + 38)
≈ 2 × (32.89 + 38)
≈ 2 × 70.89
≈ 141.78 units.
FAQ on Square Root of 1083
1.What is √1083 in its simplest form?
2.Mention the factors of 1083.
3.Calculate the square of 1083.
4.Is 1083 a prime number?
5.1083 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 1083?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1083?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1083
- Square root: A square root is the inverse of a square. For 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 is more prominent due to its use in the real world. That is why it is also known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 1083 = 3 × 3 × 3 × 3 × 13.
- Long division method: A step-by-step method used to find the square root of a non-perfect square by grouping and dividing the number methodically.
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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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