102 LearnersLast updated on May 26th, 2025
Square Root of 2.04
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 2.04.
What is the Square Root of 2.04?
The square root is the inverse of the square of the number. 2.04 is not a perfect square. The square root of 2.04 is expressed in both radical and exponential form. In radical form, it is expressed as √2.04, whereas in exponential form it is (2.04)^(1/2). √2.04 ≈ 1.428, 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 2.04
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 about these methods:
- Long division method
- Approximation method
Square Root of 2.04 by Prime Factorization Method
The prime factorization method is typically used for whole numbers, and since 2.04 is not a whole number, this method is not applicable. Instead, we consider alternative methods such as long division or approximation for non-perfect squares.
Square Root of 2.04 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 pairing the numbers from right to left. For 2.04, consider it as 204 by multiplying by 100 to remove the decimal.
Step 2: Find a number whose square is less than or equal to 2. In this case, it is 1 since 1 × 1 = 1.
Step 3: Subtract 1 from 2, bring down the next pair of digits (04) to make it 104.
Step 4: Double the divisor (1), making it 2, then find a digit n such that 2n × n is less than or equal to 104. The digit n is 4, as 24 × 4 = 96.
Step 5: Subtract 96 from 104, the remainder is 8.
Step 6: Continue the process by bringing down pairs of zeros, and repeating similar steps to get a more accurate value. So the square root of √2.04 ≈ 1.428.
Square Root of 2.04 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to estimate the square root of a given number. Now, let us learn how to find the square root of 2.04 using the approximation method.
Step 1: Find the closest perfect squares around 2.04. The closest perfect squares are 1 (1²) and 4 (2²). √2.04 falls between 1 and 2.
Step 2: Use interpolation to approximate the value between these two numbers. Using the formula (Given number - smallest perfect square) ÷ (Larger perfect square - smallest perfect square), we have (2.04 - 1) ÷ (4 - 1) ≈ 0.346. Adding this to the integer part, we get 1 + 0.346 ≈ 1.428. Thus, the square root of 2.04 is approximately 1.428.
Common Mistakes and How to Avoid Them in the Square Root of 2.04
Students make various mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes 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 usually consider only the positive square root for most practical applications.
For example, √50 = 7.07; there is also -7.07, which should not be forgotten.
Square Root of 2.04 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2.04?
The area of the square is approximately 2.04 square units.
Explanation
The area of a square = side².
The side length is given as √2.04.
Area of the square = (√2.04)² = 2.04.
Therefore, the area of the square box is approximately 2.04 square units.
Problem 2
A square-shaped plot measuring 2.04 square meters is built; if each of the sides is √2.04, what will be the square meters of half of the plot?
1.02 square meters
Explanation
We can divide the given area by 2 as the plot is square-shaped.
Dividing 2.04 by 2, we get 1.02.
So half of the plot measures 1.02 square meters.
Problem 3
Calculate √2.04 × 5.
Approximately 7.14
Explanation
The first step is to find the square root of 2.04, which is approximately 1.428.
The second step is to multiply 1.428 by 5.
So, 1.428 × 5 ≈ 7.14.
Problem 4
What will be the square root of (2.04 + 1)?
The square root is approximately 1.732.
Explanation
To find the square root, first find the sum of (2.04 + 1).
2.04 + 1 = 3.04, and then √3.04 ≈ 1.732.
Therefore, the square root of (2.04 + 1) is approximately ±1.732.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2.04 units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 8.856 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2.04 + 3)
≈ 2 × (1.428 + 3)
≈ 2 × 4.428
≈ 8.856 units.
FAQ on Square Root of 2.04
1.What is √2.04 in its simplest form?
2.Is 2.04 a perfect square?
3.Calculate the square of 2.04.
4.Is 2.04 a rational number?
5.What is the approximate value of √2.04?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 2.04?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 2.04?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 2.04
- Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction, meaning it cannot be written in the form of p/q, where q is not zero and p and q are integers.
- Principal square root: Though a number has both positive and negative square roots, the positive square root is often used in practical applications. This is known as the principal square root.
- Rational number: A rational number can be expressed as a fraction or ratio of two integers, where the denominator is not zero.
- Decimal: A decimal is a number that includes a whole number and a fractional part, represented with a decimal point, such as 7.86, 8.65, or 9.42.
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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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