117 LearnersLast updated on May 26th, 2025
Square Root of 1136
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 1136.
What is the Square Root of 1136?
The square root is the inverse of the square of the number. 1136 is not a perfect square. The square root of 1136 is expressed in both radical and exponential form. In the radical form, it is expressed as √1136, whereas (1136)^(1/2) in the exponential form. √1136 ≈ 33.694, 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 1136
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1136 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1136 is broken down into its prime factors.
Step 1: Finding the prime factors of 1136 Breaking it down, we get 2 x 2 x 2 x 2 x 71: 2^4 x 71
Step 2: Now we found out the prime factors of 1136. The second step is to make pairs of those prime factors. Since 1136 is not a perfect square, the digits of the number can’t be grouped into pairs to result in a whole number square root. Therefore, calculating 1136 using prime factorization doesn't yield an integer.
Square Root of 1136 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, group the numbers from right to left. In the case of 1136, we need to group it as 11 and 36.
Step 2: Now, find a number n whose square is less than or equal to 11. We can say n is 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: Bring down the next pair, 36, making the new dividend 236. Add the old divisor (3) with itself (3 + 3) to get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. We get 6n as the new divisor; we need to find the value of n.
Step 5: Find 6n × n ≤ 236. Let us consider n as 3, now 63 × 3 = 189.
Step 6: Subtract 189 from 236, the difference is 47, and the quotient is 33.
Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 4700.
Step 8: Now find the new divisor. It will be 67 because 673 × 3 = 2019.
Step 9: Subtracting 2019 from 4700, we get the result 2681.
Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √1136 ≈ 33.694.
Square Root of 1136 by Approximation Method
The approximation method is another method for finding 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 1136 using the approximation method.
Step 1: Find the closest perfect squares around √1136. The closest perfect square less than 1136 is 1089 (33^2), and the closest perfect square greater than 1136 is 1156 (34^2). √1136 falls between 33 and 34.
Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using the formula (1136 - 1089) ÷ (1156 - 1089) = 47 ÷ 67 ≈ 0.701. Adding 33 + 0.701 = 33.701, so the square root of 1136 is approximately 33.701.
Common Mistakes and How to Avoid Them in the Square Root of 1136
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 take only the positive square root, as it is the required one in most contexts.
For example: √50 = 7.071, 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 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 a wrong method of using roots. The right way of using roots 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 ≈ 7.071.
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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1136 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1136?
The area of the square is 1136 square units.
Explanation
The area of the square = side^2.
The side length is given as √1136.
Area of the square = side^2 = √1136 x √1136 = 1136.
Therefore, the area of the square box is 1136 square units.
Problem 2
A square-shaped building measuring 1136 square feet is built; if each of the sides is √1136, what will be the square feet of half of the building?
568 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1136 by 2, we get 568.
So half of the building measures 568 square feet.
Problem 3
Calculate √1136 x 5.
168.47
Explanation
The first step is to find the square root of 1136, which is approximately 33.694.
The second step is to multiply 33.694 by 5.
So, 33.694 x 5 ≈ 168.47.
Problem 4
What will be the square root of (1136 + 64)?
The square root is 36
Explanation
To find the square root, we need to find the sum of (1136 + 64). 1136 + 64 = 1200, and then √1200 ≈ 34.64. Therefore, the square root of (1136 + 64) is approximately ±34.64.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1136 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 167.388 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1136 + 50) = 2 × (33.694 + 50) = 2 × 83.694 = 167.388 units.
FAQ on Square Root of 1136
1.What is √1136 in its simplest form?
2.Mention the factors of 1136.
3.Calculate the square of 1136.
4.Is 1136 a prime number?
5.1136 is divisible by?
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 1136?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1136?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1136
- 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.
- 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 real-world applications. Hence, it is known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3^2.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number into pairs of digits from right to left and performing division similar to long division of numbers.
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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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