123 LearnersLast updated on May 26th, 2025
Square Root of 1183
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1183.
What is the Square Root of 1183?
The square root is the inverse of the square of the number. 1183 is not a perfect square. The square root of 1183 is expressed in both radical and exponential form. In the radical form, it is expressed as √1183, whereas (1183)^(1/2) in the exponential form. √1183 ≈ 34.39882, 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 1183
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the 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 1183 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1183 is broken down into its prime factors.
Step 1: Finding the prime factors of 1183. Breaking it down, we get 1183 = 7 x 169, which further breaks down to 7 x 13 x 13: 7^1 x 13^2.
Step 2: Now we have found the prime factors of 1183. The second step is to make pairs of those prime factors. Since 1183 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1183 using prime factorization is not straightforward.
Square Root of 1183 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 1183, we need to group it as 83 and 11.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n as ‘3’ because 3 x 3 = 9, which is less than or equal to 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Now let us bring down 83, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be 6n, where we need to find the value of n such that 6n x n is less than or equal to 283. Let n be 4, so 64 x 4 = 256.
Step 5: Subtract 256 from 283, the difference is 27, and the quotient is 34.
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 zeros to the dividend. Now the new dividend is 2700.
Step 7: Now we need to find the new divisor, 688, such that 688 x 4 = 2752.
Step 8: Subtracting 2752 from 2700 gives us a negative number, so we adjust n to 3. Thus, 683 x 3 = 2049.
Step 9: Subtracting 2049 from 2700, we get the result as 651.
Step 10: Now the quotient is 34.3.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.
So the square root of √1183 is approximately 34.40.
Square Root of 1183 by Approximation Method
The approximation method is another method for finding the 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 1183 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1183. The smallest perfect square less than 1183 is 1156, and the largest perfect square more than 1183 is 1225. √1183 falls somewhere between 34 and 35.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1183 - 1156) ÷ (1225 - 1156) = 27 ÷ 69 ≈ 0.3913. 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 34 + 0.3913 = 34.3913, so the square root of 1183 is approximately 34.40.
Common Mistakes and How to Avoid Them in the Square Root of 1183
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol 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, √(12 + 24) = √12 + √24 is the wrong method. The right 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 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, √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. This may either happen in subtraction or elsewhere.
Square root of 1183 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1183?
The area of the square is approximately 1183 square units.
Explanation
The area of the square = side^2. The side length is given as √1183. Area of the square = side^2 = √1183 x √1183 = 1183. Therefore, the area of the square box is approximately 1183 square units.
Problem 2
A square-shaped building measuring 1183 square feet is built; if each of the sides is √1183, what will be the square feet of half of the building?
591.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 1183 by 2 = we get 591.5. So half of the building measures 591.5 square feet.
Problem 3
Calculate √1183 x 5.
171.9941
Explanation
The first step is to find the square root of 1183, which is approximately 34.39882, the second step is to multiply 34.39882 by 5. So 34.39882 x 5 ≈ 171.9941.
Problem 4
What will be the square root of (1183 + 17)?
The square root is approximately 35.
Explanation
To find the square root, we need to find the sum of (1183 + 17). 1183 + 17 = 1200, and then √1200 ≈ 34.641. Therefore, the square root of (1183 + 17) is approximately 34.641.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1183 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 145.60 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1183 + 38) = 2 × (34.39882 + 38) = 2 × 72.39882 ≈ 144.79764 units.
FAQ on Square Root of 1183
1.What is √1183 in its simplest form?
2.Mention the factors of 1183.
3.Calculate the square of 1183.
4.Is 1183 a prime number?
5.1183 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 1183?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1183?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 1183
- 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, √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. That is why it is also known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A step-by-step method for finding the square root of a non-perfect square number.
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Jaskaran Singh Saluja
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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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