101 LearnersLast updated on May 26th, 2025
Square Root of 1.04
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 1.04.
What is the Square Root of 1.04?
The square root is the inverse of the square of the number. 1.04 is not a perfect square. The square root of 1.04 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.04, whereas (1.04)^(1/2) in the exponential form. √1.04 ≈ 1.0198, 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 1.04
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 1.04 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. However, since 1.04 is a decimal, we can't directly apply prime factorization in the traditional sense used for integers. Thus, calculating 1.04 using prime factorization is not feasible.
Square Root of 1.04 by Long Division Method
The long division method is particularly used for non-perfect square numbers, including decimals. Let us now learn how to find the square root of 1.04 using the long division method, step by step:
Step 1: Consider 1.04 as 104 by moving the decimal two places to the right. Group the digits in pairs from right to left.
Step 2: Find a number whose square is less than or equal to 1. The number is 1. Subtract 1 from 1 to get a remainder of 0.
Step 3: Bring down the next pair of digits, which is 04, to make it 104. Double the current quotient (1), resulting in 2, and use it as the new divisor.
Step 4: Determine a digit n such that 2n × n ≤ 104. The suitable digit is 4.
Step 5: Subtract 104 from 104 to get a remainder of 0. Since we have reached the decimal point, place a decimal in the quotient.
Step 6: The quotient now is 1.0. Continue the process to refine the decimal places as needed.
The square root of 1.04 is approximately 1.0198.
Square Root of 1.04 by Approximation Method
The approximation method is another approach for finding square roots, especially for decimals. Let us learn how to find the square root of 1.04 using approximation:
Step 1: Identify the perfect squares around 1.04. The closest perfect squares are 1 (1^2) and 1.21 (1.1^2). Therefore, √1.04 is between 1 and 1.1.
Step 2: Use interpolation or successive approximation to refine the square root value. A rough estimate of the decimal value between 1 and 1.1 gives √1.04 ≈ 1.0198.
Common Mistakes and How to Avoid Them in the Square Root of 1.04
Students often make mistakes while finding square roots, such as overlooking the negative square root or skipping steps in methods like long division. Let us explore common mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It is crucial to remember that a number has both positive and negative square roots. However, usually, only the positive square root is considered in practical applications.
For example, √1.04 ≈ 1.0198, and -1.0198 is also a valid square root.
Square Root of 1.04 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.04?
The area of the square is 1.081 square units.
Explanation
The area of the square = side².
The side length is given as √1.04.
Area of the square = (√1.04)² = 1.04.
Therefore, the area of the square box is 1.04 square units.
Problem 2
A square-shaped garden measures 1.04 square meters. If each side is √1.04 meters, what is the length of the garden's diagonal?
Approximately 1.442 meters.
Explanation
The diagonal of a square with side length s is given by s√2.
Diagonal = √1.04 × √2 ≈ 1.0198 × 1.414 ≈ 1.442 meters.
Problem 3
Calculate √1.04 × 10.
Approximately 10.198.
Explanation
First, find the square root of 1.04, which is approximately 1.0198.
Multiply by 10. So, 1.0198 × 10 ≈ 10.198.
Problem 4
What is the square root of (1.04 + 0.01)?
The square root is approximately 1.05.
Explanation
Calculate (1.04 + 0.01) = 1.05.
Then, the square root of 1.05 is approximately 1.0247.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1.04 meters and the width ‘w’ is 1 meter.
Approximately 4.0396 meters.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.04 + 1) ≈ 2 × (1.0198 + 1) ≈ 2 × 2.0198 ≈ 4.0396 meters.
FAQ on Square Root of 1.04
1.What is √1.04 in its simplest form?
2.What is the decimal approximation of √1.04?
3.What are the nearest perfect squares to 1.04?
4.Is 1.04 a perfect square?
5.What is the square of √1.04?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 1.04?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 1.04?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 1.04
- Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse operation is the square root: √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers, such as √1.04.
- Decimal: A decimal is a number with a whole part and a fractional part separated by a decimal point, such as 1.04.
- Perfect square: A perfect square is a number that is the square of an integer, such as 4 (2²).
- Long division method: A technique used to find square roots of non-perfect squares by dividing the number into pairs of digits and determining the root step by step.
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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.
