105 LearnersLast updated on May 26th, 2025
Square Root of 0.09
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 0.09.
What is the Square Root of 0.09?
The square root is the inverse of the square of the number. 0.09 is a perfect square. The square root of 0.09 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.09, whereas (0.09)^(1/2) in the exponential form. √0.09 = 0.3, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 0.09
The prime factorization method is typically used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are used. However, since 0.09 is a perfect square, we can easily find its square root. Let us now learn the following methods: Prime factorization method Long division method Approximation method
Square Root of 0.09 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 0.09 is broken down into its prime factors: Step 1: Express 0.09 as a fraction: 0.09 = 9/100. Step 2: Break down the numerator and the denominator: 9 = 3 × 3 and 100 = 10 × 10. Step 3: Now, the prime factorization of 9/100 is (3 × 3)/(10 × 10). Step 4: Take the square root of both the numerator and the denominator: √(3 × 3)/√(10 × 10) = 3/10 = 0.3.
Square Root of 0.09 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also verify the square root of perfect squares. Here, we find the square root using the long division method, step by step: Step 1: To begin with, write 0.09 in decimal form, digits on the right will be grouped as 09. Step 2: Find a number whose square is less than or equal to 09. We know 3 × 3 = 09. Step 3: The quotient is 0.3, which is the square root of 0.09.
Square Root of 0.09 by Approximation Method
The approximation method is another method for finding square roots, especially useful for non-perfect squares. Since 0.09 is a perfect square, we can directly find: Step 1: Recognize that 0.09 is close to 0.1. Step 2: The square root of 0.09 is exactly 0.3, as calculated previously.
Common Mistakes and How to Avoid Them in the Square Root of 0.09
Students often make mistakes while finding the square root, such as confusing decimals or misplacing the square root sign. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Ignoring Decimal Places
It's crucial to maintain the correct number of decimal places when dealing with decimals. For example, √0.09 should be calculated accurately as 0.3, not simply 3.
Square Root of 0.09 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.64?
The area of the square is 0.4096 square units.
Explanation
The area of the square = side². The side length is given as √0.64. Area of the square = side² = √0.64 x √0.64 = 0.8 × 0.8 = 0.64. Therefore, the area of the square box is 0.64 square units.
Problem 2
A square-shaped building measuring 0.09 square feet is built; if each of the sides is √0.09, what will be the square feet of half of the building?
0.045 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 0.09 by 2, we get 0.045. So half of the building measures 0.045 square feet.
Problem 3
Calculate √0.09 x 5.
1.5
Explanation
The first step is to find the square root of 0.09, which is 0.3, and the second step is to multiply 0.3 by 5. So 0.3 x 5 = 1.5.
Problem 4
What will be the square root of (0.04 + 0.05)?
The square root is 0.3.
Explanation
To find the square root, we need to find the sum of (0.04 + 0.05). 0.04 + 0.05 = 0.09, and then √0.09 = 0.3. Therefore, the square root of (0.04 + 0.05) is ±0.3.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √0.36 units and the width ‘w’ is 0.38 units.
We find the perimeter of the rectangle as 1.46 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√0.36 + 0.38) = 2 × (0.6 + 0.38) = 2 × 0.98 = 1.96 units.
FAQ on Square Root of 0.09
1.What is √0.09 in its simplest form?
2.Mention the factors of 0.09.
3.Calculate the square of 0.3.
4.Is 0.09 a perfect square?
5.Is 0.09 divisible by any integer?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 0.09?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 0.09?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 0.09
- Square root: A square root is the inverse of a square. Example: 0.3² = 0.09 and the inverse of the square is the square root that is √0.09 = 0.3.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. Example: 9 is a perfect square because it is 3 × 3.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Fraction: A fraction represents a part of a whole or any number of equal parts. Example: 1/2, 3/4, 9/100 are fractions.
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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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