102 LearnersLast updated on May 26th, 2025
Square Root of 1169
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 1169.
What is the Square Root of 1169?
The square root is the inverse of the square of the number. 1169 is not a perfect square. The square root of 1169 is expressed in both radical and exponential form. In the radical form, it is expressed as √1169, whereas (1169)^(1/2) in the exponential form. √1169 ≈ 34.187, 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 1169
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 1169 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1169 is broken down into its prime factors.
Step 1: Finding the prime factors of 1169 Breaking it down, we get 1169 = 29 x 29 x 1.
Step 2: Now we found out the prime factors of 1169. The second step is to make pairs of those prime factors. Since 1169 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1169 using prime factorization is challenging for finding exact roots but helps in approximation.
Square Root of 1169 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 1169, we need to group it as 69 and 11.
Step 2: Now we need to find n whose square is closest to 11. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 11. Now the quotient is 3 after subtracting 9 from 11, the remainder is 2.
Step 3: Now let us bring down 69 which is the new dividend. Add the old divisor with the same number 3 + 3, 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, we need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 269. Let us consider n as 4, now 64 x 4 = 256.
Step 6: Subtract 269 from 256, the difference is 13, and the quotient is 34.
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 1300.
Step 8: Now we need to find the new divisor that is 684 because 684 x 2 = 1368
Step 9: Subtracting 1368 from 1300, we get -68.
Step 10: Now the quotient is approximately 34.1.
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 √1169 is approximately 34.19.
Square Root of 1169 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 1169 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1169. The smallest perfect square less than 1169 is 1156 (34^2) and the closest perfect square more than 1169 is 1225 (35^2). √1169 falls somewhere between 34 and 35.
Step 2: Now we need to apply the formula that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (1169 - 1156) ÷ (1225 - 1156) ≈ 0.19 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 + 0.19 = 34.19, so the square root of 1169 is approximately 34.19.
Common Mistakes and How to Avoid Them in the Square Root of 1169
Students do make mistakes while finding the square root, such as forgetting about the negative square root or 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, there is also -7.07 which should not be forgotten.
Square Root of 1169 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1169?
The area of the square is approximately 1368.472 square units.
Explanation
The area of the square = side^2.
The side length is given as √1169.
Area of the square = side^2 = √1169 x √1169 ≈ 34.19 x 34.19 ≈ 1169.
Therefore, the area of the square box is approximately 1169 square units.
Problem 2
A square-shaped building measuring 1169 square feet is built; if each of the sides is √1169, what will be the square feet of half of the building?
584.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1169 by 2 = we get 584.5.
So half of the building measures 584.5 square feet.
Problem 3
Calculate √1169 x 5.
Approximately 170.95
Explanation
The first step is to find the square root of 1169 which is approximately 34.19, the second step is to multiply 34.19 with 5. So 34.19 x 5 ≈ 170.95.
Problem 4
What will be the square root of (1156 + 13)?
The square root is approximately 34.19.
Explanation
To find the square root, we need to find the sum of (1156 + 13). 1156 + 13 = 1169, and the square root of 1169 is approximately 34.19. Therefore, the square root of (1156 + 13) is approximately ±34.19.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1169 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 144.38 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1169 + 38) ≈ 2 × (34.19 + 38) ≈ 2 × 72.19 ≈ 144.38 units.
FAQ on Square Root of 1169
1.What is √1169 in its simplest form?
2.Mention the factors of 1169.
3.Calculate the square of 1169.
4.Is 1169 a prime number?
5.1169 is divisible by what numbers?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1169?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1169?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1169
- 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 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.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
- Approximation: A method used to find an estimate close to the actual value. It is often used when the value cannot be calculated exactly.
- Long division method: A technique used to find the square root of non-perfect squares by dividing and averaging.
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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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