117 LearnersLast updated on May 26th, 2025
Square Root of 111.68
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 111.68.
What is the Square Root of 111.68?
The square root is the inverse of the square of the number. 111.68 is not a perfect square. The square root of 111.68 is expressed in both radical and exponential form.
In the radical form, it is expressed as √111.68, whereas (111.68)(1/2) in the exponential form. √111.68 ≈ 10.56817, 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 111.68
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 111.68 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. However, since 111.68 is not an integer, we cannot directly use prime factorization. Therefore, calculating 111.68 using prime factorization is inappropriate.
Square Root of 111.68 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 digits of 111.68 from right to left as 11|16|80.
Step 2: Find the largest number whose square is less than or equal to 11, which is 3 (since 3^2 = 9). Subtract 9 from 11 to get a remainder of 2, and bring down 16 to make it 216.
Step 3: Double the divisor (3), making it 6, and find a digit x such that 6x × x ≤ 216. The suitable x is 3, since 63 × 3 = 189. Subtract 189 from 216 to get 27, and bring down 80 to make it 2780.
Step 4: Double the current divisor (63), making it 126, and find a digit y such that 126y × y ≤ 2780. The suitable y is 2, since 1262 × 2 = 2524. Subtract 2524 from 2780 to get 256.
Step 5: Continue the process to get more decimal places.
The square root of 111.68 is approximately 10.568.
Square Root of 111.68 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Let us learn how to find the square root of 111.68 using the approximation method:
Step 1: Identify the perfect squares nearest to 111.68, which are 100 (10^2) and 121 (11^2). Therefore, √111.68 falls between 10 and 11.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). For 111.68: (111.68 - 100) / (121 - 100) = 11.68 / 21 ≈ 0.556.
Step 3: Add this decimal value to the smaller root: 10 + 0.556 = 10.556.
Therefore, the square root of 111.68 is approximately 10.556.
Common Mistakes and How to Avoid Them in the Square Root of 111.68
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically take only the positive square root, as it is the one required in many real-world applications.
For example: √64 = 8, but there is also -8.
Square Root of 111.68 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √111.68?
The area of the square is approximately 111.68 square units.
Explanation
The area of the square = side2.
The side length is given as √111.68.
Area of the square = (√111.68) × (√111.68) = 111.68 square units.
Therefore, the area of the square box is approximately 111.68 square units.
Problem 2
A square-shaped building measuring 111.68 square feet is built; if each of the sides is √111.68, what will be the square feet of half of the building?
55.84 square feet
Explanation
We can divide the given area by 2, as the building is square-shaped.
Dividing 111.68 by 2 gives us 55.84.
So half of the building measures 55.84 square feet.
Problem 3
Calculate √111.68 × 5.
Approximately 52.84
Explanation
First, find the square root of 111.68, which is approximately 10.568.
Multiply 10.568 by 5.
So, 10.568 × 5 ≈ 52.84.
Problem 4
What will be the square root of (101.68 + 10)?
The square root is approximately 11.
Explanation
To find the square root, first calculate the sum of (101.68 + 10). 101.68 + 10 = 111.68, and then √111.68 ≈ 10.568.
Therefore, the square root of (101.68 + 10) is approximately ±10.568.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √111.68 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 61.14 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√111.68 + 20)
= 2 × (10.568 + 20)
= 2 × 30.568
= 61.136 units (approximately 61.14 units).
FAQ on Square Root of 111.68
1.What is √111.68 in its simplest form?
2.Is 111.68 a perfect square?
3.Calculate the square of 111.68.
4.Is 111.68 a prime number?
5.What is the cube root of 111.68?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 111.68?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 111.68?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 111.68
- Square root: A square root is the inverse operation of squaring a number. For example, if 52 = 25, then the square root of 25 is 5.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction; its decimal representation is non-repeating and non-terminating.
- Radical: A symbol (√) used to denote the square root or nth root of a number.
- Decimal: A number that consists of a whole number part and a fractional part separated by a decimal point, such as 10.568.
- Approximation: The process of finding a value close to the true value, often used when dealing with irrational numbers or complex calculations.
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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
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