103 LearnersLast updated on May 26th, 2025
Square Root of 0.015
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 0.015.
What is the Square Root of 0.015?
The square root is the inverse of the square of the number. 0.015 is not a perfect square. The square root of 0.015 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.015, whereas (0.015)^(1/2) in the exponential form. √0.015 ≈ 0.12247, 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 0.015
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 0.015 by Prime Factorization Method
The prime factorization of a number is the product of its prime factors. Since 0.015 is a decimal, it is more complex to factorize directly into primes like integers. Thus, calculating 0.015 using prime factorization is not straightforward, and other methods like long division or approximation are more suitable.
Square Root of 0.015 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should find the closest perfect square number to the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Consider 0.015 as a decimal. We can convert it to 15 and find the square root of 15.
Step 2: Group the digits of 15 in pairs from right to left, here it is already a two-digit number. Start with the integral part.
Step 3: Find a number whose square is close to the number 15 without exceeding it. In this case, 3 × 3 = 9 is close to 15.
Step 4: Subtract 9 from 15 to get 6 as the remainder.
Step 5: Bring down two zeros to make it 600, and double the divisor 3 to make it 6, forming 60 as the new divisor.
Step 6: Find a digit n such that 60n × n is less than or equal to 600. Here, n = 9 fits, as 609 is too large.
Step 7: Subtract 540 from 600 to get 60 as the remainder, bring down two more zeros.
Step 8: Repeat the process to find the next digits after the decimal point.
Thus, the square root of 0.015 is approximately 0.12247.
Square Root of 0.015 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 0.015 using the approximation method.
Step 1: Consider 0.015. We can approximate the square root by finding square roots of nearby values.
Step 2: We know √0.01 = 0.1 and √0.04 = 0.2. So, √0.015 will fall between 0.1 and 0.2.
Step 3: Using linear approximation, we can find that √0.015 is closer to 0.12247.
Thus, the approximate square root of 0.015 is 0.12247.
Common Mistakes and How to Avoid Them in the Square Root of 0.015
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example, √0.015 ≈ 0.12247, there is also -0.12247 which should not be forgotten.
Square Root of 0.015 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.009?
The area of the square is 0.009 square units.
Explanation
The area of the square = side^2.
The side length is given as √0.009.
Area of the square = side^2
= √0.009 × √0.009
= 0.03 × 0.03
= 0.009.
Therefore, the area of the square box is 0.009 square units.
Problem 2
A square-shaped building measuring 0.015 square meters is built; if each of the sides is √0.015, what will be the square meters of half of the building?
0.0075 square meters
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 0.015 by 2 = we get 0.0075.
So half of the building measures 0.0075 square meters.
Problem 3
Calculate √0.015 × 5.
0.61235
Explanation
The first step is to find the square root of 0.015, which is approximately 0.12247.
The second step is to multiply 0.12247 by 5.
So, 0.12247 × 5 ≈ 0.61235.
Problem 4
What will be the square root of (0.01 + 0.005)?
The square root is approximately 0.12247.
Explanation
To find the square root, we need to find the sum of (0.01 + 0.005). 0.01 + 0.005 = 0.015, and then √0.015 ≈ 0.12247.
Therefore, the square root of (0.01 + 0.005) is approximately ±0.12247.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √0.02 units and the width ‘w’ is 0.03 units.
We find the perimeter of the rectangle as 0.4849 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√0.02 + 0.03)
= 2 × (0.14142 + 0.03)
≈ 2 × 0.17142
≈ 0.34284 units.
FAQ on Square Root of 0.015
1.What is √0.015 in its simplest form?
2.How do you find the square root of a decimal like 0.015?
3.Calculate the square of 0.015.
4.Is 0.015 a perfect square?
5.What are some nearby perfect squares to 0.015?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 0.015?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 0.015?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 0.015
- Square root: A square root is the inverse operation of squaring a number. For example, if 4^2 = 16, then the square root of 16 is √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed exactly as a simple fraction. It has a non-repeating and non-terminating decimal expansion, such as √0.015.
- Decimal: A decimal is a number that includes a decimal point followed by digits showing values less than one, such as 0.015.
- Approximation: Approximation involves estimating a value or calculation that is not exact but close enough to be useful, such as estimating √0.015 ≈ 0.12247.
- Long division: Long division is a step-by-step method for dividing multi-digit numbers, often used to find the square roots of non-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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