102 LearnersLast updated on May 26th, 2025
Square Root of 1.13
If a number is multiplied by itself, 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 1.13.
What is the Square Root of 1.13?
The square root is the inverse of the square of the number. 1.13 is not a perfect square. The square root of 1.13 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1.13, whereas in the exponential form it is (1.13)^(1/2). √1.13 ≈ 1.063, 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 1.13
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 1.13 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Using this method, we can find the square root of 1.13 step by step.
Step 1: To begin with, we need to convert 1.13 into a fraction, which is 113/100.
Step 2: Now we need to find the square root of 113/100. The closest perfect squares for 113 are 100 and 121, and for 100 it is 100 itself.
Step 3: Using long division, we find that the square root of 113 is approximately 10.6301.
Step 4: The square root of 100 is exactly 10.
Step 5: Therefore, √(113/100) = 10.6301/10 = 1.06301.
So the square root of √1.13 is approximately 1.063.
Square Root of 1.13 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to approximate the square root of 1.13.
Step 1: Identify two perfect squares between which 1.13 lies. The closest are 1 (1^2) and 1.21 (1.1^2).
Step 2: Since 1.13 is between 1 and 1.21, √1.13 lies between 1 and 1.1.
Step 3: By further approximation, √1.13 ≈ 1.063.
Thus, the square root of 1.13 is approximately 1.063.
Common Mistakes and How to Avoid Them in the Square Root of 1.13
Students make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in the long division method. Now let us look at a few common mistakes 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 usually take the positive square root, as it is the principal one.
For example: √1.13 = ±1.063, but we focus on the positive 1.063.
Square Root of 1.13 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.13?
The area of the square is approximately 1.13 square units.
Explanation
The area of the square = side².
The side length is given as √1.13.
Area of the square = side² = √1.13 × √1.13 ≈ 1.063 × 1.063 ≈ 1.13.
Therefore, the area of the square box is approximately 1.13 square units.
Problem 2
A square-shaped building measuring 1.13 square feet is built; if each of the sides is √1.13, what will be the square feet of half of the building?
Approximately 0.565 square feet.
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 1.13 by 2 = we get approximately 0.565.
So half of the building measures approximately 0.565 square feet.
Problem 3
Calculate √1.13 × 5.
Approximately 5.315.
Explanation
The first step is to find the square root of 1.13 which is approximately 1.063.
The second step is to multiply 1.063 with 5. So 1.063 × 5 ≈ 5.315.
Problem 4
What will be the square root of (1.13 + 0.07)?
The square root is approximately ±1.1.
Explanation
To find the square root, we need to find the sum of (1.13 + 0.07). 1.13 + 0.07 = 1.2, and then √1.2 ≈ ±1.095.
Therefore, the square root of (1.13 + 0.07) is approximately ±1.095.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1.13 units and the width ‘w’ is 2 units.
The perimeter of the rectangle is approximately 6.126 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.13 + 2) = 2 × (1.063 + 2) = 2 × 3.063 ≈ 6.126 units.
FAQ on Square Root of 1.13
1.What is √1.13 in its simplest form?
2.How do you calculate the square root of 1.13?
3.Is 1.13 a perfect square?
4.What is the decimal representation of √1.13?
5.Can √1.13 be expressed as a fraction?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 1.13?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 1.13?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 1.13
- Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 1.063² ≈ 1.13.
- Irrational number: An irrational number cannot be expressed as a fraction of two integers. Example: √1.13 is irrational.
- Approximation: Approximating a number means finding a value that is close to the exact value, often used when the exact value is difficult to determine.
- Long division method: A procedure for dividing numbers to find an approximate value of their square root, especially useful for non-perfect squares.
- Decimal: A number that includes a whole number and a fractional part separated by a decimal point. Example: 1.063 is a decimal.
Explore More algebra
Previous to Square Root of 1.13
About BrightChamps in Bahrain
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
