100 LearnersLast updated on May 26th, 2025
Square Root of 1.03
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 1.03.
What is the Square Root of 1.03?
The square root is the inverse operation of squaring a number. 1.03 is not a perfect square. The square root of 1.03 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.03, whereas as (1.03)^(1/2) in exponential form. √1.03 ≈ 1.01489, which is an irrational number because it cannot be expressed as a ratio of integers.
Finding the Square Root of 1.03
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 1.03, the long-division method and approximation method are used. Let us now learn these methods:
- Long-division method
- Approximation method
Square Root of 1.03 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: Start by placing a decimal point in your quotient and pairing the digits of the number 1.03 from the decimal point outwards. This means looking at 1 and 03 separately.
Step 2: Find a number whose square is closest to 1 but not greater than 1. The number is 1 because 1 × 1 = 1.
Step 3: Subtract 1 from 1 and bring down the next pair of digits, making it 03.
Step 4: Double the divisor (which is 1) to get 2. Use this as the new divisor base.
Step 5: Find a digit to append to 2 to form a divisor that divides 03 as closely as possible without exceeding it. This digit is 0, so the new divisor is 20, and the quotient is 1.0.
Step 6: Multiply 20 by 0 and subtract from 03 to get 03. Append two zeros to continue.
Step 7: Repeat these steps until you reach a sufficient level of precision, achieving a value of approximately 1.01489.
Square Root of 1.03 by Approximation Method
Approximation is a simple method for finding square roots. Now let us learn how to find the square root of 1.03 using this method.
Step 1: Identify two perfect squares between which 1.03 lies. The closest perfect squares around 1.03 are 1 (1^2) and 1.21 (1.1^2).
Step 2: Apply the approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square)
Step 3: Using this formula: (1.03 - 1) / (1.21 - 1) = 0.03 / 0.21 ≈ 0.142857.
Step 4: Add this result to the square root of the smaller perfect square to get an approximation: 1 + 0.0142857 ≈ 1.01429
Thus, the square root of 1.03 is approximately 1.01489.
Common Mistakes and How to Avoid Them in the Square Root of 1.03
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in methods, etc. Here are a few mistakes to be aware of:
Mistake 1
Forgetting about the negative square root
Students should be reminded that every number has both positive and negative square roots. However, we typically consider only the positive square root in practical applications.
For example: √1.03 ≈ ±1.01489.
Square Root of 1.03 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.03?
The area of the square is approximately 1.0302 square units.
Explanation
The area of the square = side^2.
The side length is given as √1.03.
Area of the square = (√1.03) × (√1.03) = 1.01489 × 1.01489 ≈ 1.0302.
Therefore, the area of the square box is approximately 1.0302 square units.
Problem 2
A square-shaped building measuring 1.03 square meters is built; if each of the sides is √1.03, what will be the square meters of half of the building?
0.515 square meters
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1.03 by 2 gives us 0.515.
So half of the building measures 0.515 square meters.
Problem 3
Calculate √1.03 × 5.
5.07445
Explanation
First, find the square root of 1.03, which is approximately 1.01489.
Then multiply 1.01489 by 5. So, 1.01489 × 5 ≈ 5.07445.
Problem 4
What will be the square root of (1 + 0.03)?
The square root is approximately 1.01489.
Explanation
To find the square root, we need to find the sum of (1 + 0.03) = 1.03, and then √1.03 ≈ 1.01489.
Therefore, the square root of (1 + 0.03) is approximately ±1.01489.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1.03 units and the width ‘w’ is 0.5 units.
The perimeter of the rectangle is approximately 3.02978 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.03 + 0.5) ≈ 2 × (1.01489 + 0.5) = 2 × 1.51489 ≈ 3.02978 units.
FAQ on Square Root of 1.03
1.What is √1.03 in its simplest form?
2.What are the factors of 1.03?
3.Calculate the square of 1.03.
4.Is 1.03 a prime number?
5.1.03 is divisible by?
Important Glossaries for the Square Root of 1.03
- Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse is √16 = 4.
- Irrational number: An irrational number cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
- Principal square root: A number has both positive and negative square roots, but the positive square root is typically used in practical applications, known as the principal square root.
- Decimal: A decimal number has a whole number part and a fractional part separated by a decimal point, such as 1.03.
- Approximation: Estimating a number close to the exact value, often used for non-perfect squares like √1.03.
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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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