Square Root of 1.13
2026-02-28 08:55 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1.13

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Last updated on August 5, 2025

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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √1.13?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √1.13 × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (1.13 + 0.07)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1.13 units and the width ‘w’ is 2 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 1.13

1.What is √1.13 in its simplest form?

The square root of 1.13 cannot be further simplified into a neat fractional form and is approximately 1.063.

2.How do you calculate the square root of 1.13?

The square root of 1.13 can be calculated using methods like long division or approximation, resulting in an approximate value of 1.063.

3.Is 1.13 a perfect square?

No, 1.13 is not a perfect square since it cannot be expressed as the square of an integer.

4.What is the decimal representation of √1.13?

5.Can √1.13 be expressed as a fraction?

No, because √1.13 is an irrational number, it cannot be expressed exactly as a fraction.

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.

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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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.