101 LearnersLast updated on May 26th, 2025
Square Root of 1.06
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1.06.
What is the Square Root of 1.06?
The square root is the inverse of the square of the number. 1.06 is not a perfect square. The square root of 1.06 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1.06, whereas (1.06)^(1/2) in the exponential form. √1.06 ≈ 1.029563, 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 1.06
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 1.06 by Prime Factorization Method
The prime factorization method involves expressing a number as a product of its prime numbers. Since 1.06 is not a perfect square and is a decimal, this method is not applicable directly. For non-perfect square numbers, especially decimals, other methods like the long division or approximation method are more suitable.
Square Root of 1.06 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step:
Step 1: Pair the digits of 1.06 from the decimal point. In this case, consider it as 01 and 06.
Step 2: Find a number whose square is less than or equal to 1. The closest is 1, giving a quotient of 1. Subtract 1 from 1 to get a remainder of 0.
Step 3: Bring down 06, making it the new dividend of 6. Add the old divisor with itself (1 + 1) to get a new divisor of 2.
Step 4: Find a digit n such that 2n × n is less than or equal to 6. The digit is 2, as 2 × 2 = 4.
Step 5: Subtract 4 from 6 to get 2. The quotient is now 1.2.
Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeros to make it 200.
Step 7: Find a new divisor by doubling the previous quotient (12), which is 24. Find n such that 24n × n is less than or equal to 200. The digit is 8, as 248 × 8 = 1984.
Step 8: Subtract 1984 from 2000 to get 16, and the quotient is 1.028.
Step 9: Continue this process until you achieve the desired decimal places.
So the square root of √1.06 is approximately 1.029.
Square Root of 1.06 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 1.06 using the approximation method.
Step 1: Identify perfect squares between which 1.06 falls. 1.06 is slightly greater than 1 (perfect square of 1) and less than 1.21 (perfect square of 1.1).
Step 2: Apply a linear approximation. Use the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (1.06 - 1) / (1.21 - 1) = 0.06 / 0.21 ≈ 0.2857.
Step 3: Add this to the smaller perfect square root: 1 + 0.2857 = 1.2857 (adjusted for precision, the approximation is 1.029).
Thus, the approximate square root of 1.06 is 1.029.
Common Mistakes and How to Avoid Them in the Square Root of 1.06
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
Students must remember that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is the required one in most practical scenarios.
For example: √1.06 ≈ 1.029, but there is also -1.029 which should not be forgotten.
Square Root of 1.06 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.06?
The area of the square is approximately 1.06 square units.
Explanation
The area of a square = (side)^2.
The side length is given as √1.06.
Area of the square = (√1.06)^2 = 1.06.
Therefore, the area of the square box is approximately 1.06 square units.
Problem 2
A square-shaped plot measures 1.06 square meters; if each side is √1.06, what will be the square meters of half of the plot?
0.53 square meters
Explanation
To find half of the plot's area, divide the total area by 2.
1.06 / 2 = 0.53.
So half of the plot measures 0.53 square meters.
Problem 3
Calculate √1.06 × 5.
Approximately 5.145
Explanation
First, find the square root of 1.06, which is approximately 1.029.
Then multiply 1.029 by 5. 1.029 × 5 ≈ 5.145.
Problem 4
What will be the square root of (1 + 0.06)?
The square root is 1.03
Explanation
To find the square root, calculate (1 + 0.06) = 1.06.
The square root of 1.06 is approximately 1.03.
Therefore, the square root of (1 + 0.06) is ±1.03.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1.06 units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 8.06 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√1.06 + 3) = 2 × (1.029 + 3) ≈ 2 × 4.029 = 8.06 units.
FAQ on Square Root of 1.06
1.What is √1.06 in its simplest form?
2.Is 1.06 a perfect square?
3.Is 1.06 a rational number?
4.What is the square of 1.06?
5.Can √1.06 be expressed as a fraction?
Important Glossaries for the Square Root of 1.06
- 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.
- Decimal: If a number has a whole number and a fractional part in a single number, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Long division method: A method used to find the square root of a number by dividing it into pairs of numbers and finding the root step-by-step.
- Approximation method: A method to estimate the square root of a non-perfect square by comparing it to nearby perfect squares.
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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.
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