113 LearnersLast updated on May 26th, 2025
Square Root of 0.05
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 0.05.
What is the Square Root of 0.05?
The square root is the inverse of the square of a number. 0.05 is not a perfect square. The square root of 0.05 is expressed in both radical and exponential form. In radical form, it is expressed as √0.05, whereas (0.05)^(1/2) in the exponential form. √0.05 ≈ 0.2236, 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 0.05
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 0.05 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Since 0.05 is not a whole number, we cannot directly use prime factorization in the traditional sense. Instead, we convert to a fraction:
Step 1: Express 0.05 as a fraction: 0.05 = 5/100 = 1/20
Step 2: Prime factorize 20: 20 = 2 x 2 x 5
Step 3: Therefore, √0.05 = √(1/20) = √(1/(22 x 5)) = 1/(2√5)
Square Root of 0.05 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: First, convert 0.05 to 5/100 and then to 0.05 for division.
Step 2: Group the digits from right to left. Here, we'll work with 0.0500, grouping as 05 and 00.
Step 3: Find a number whose square is less than or equal to the first group (05). That number is 2, as 2 x 2 = 4.
Step 4: Subtract 4 from 5, giving a remainder of 1.
Step 5: Bring down the next two zeros, making the new dividend 100.
Step 6: Double the divisor (which is 2), making it 4.
Step 7: Determine the next digit in the quotient (n), such that 4n x n ≤ 100. The number is 2, as 42 x 2 = 84.
Step 8: Subtract 84 from 100 to get 16, and bring down another pair of zeros.
Step 9: Continue this process until the desired accuracy is achieved.
Square Root of 0.05 by Approximation Method
The approximation method is another method for finding square roots, which is an easy way to find the square root of a given number. Let's see how to find the square root of 0.05 using the approximation method.
Step 1: Identify the perfect squares closest to 0.05. The perfect squares are 0.04 (√0.04 = 0.2) and 0.09 (√0.09 = 0.3).
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (0.05 - 0.04) / (0.09 - 0.04) = 0.01 / 0.05 = 0.2 Adding the value to the initial smaller root: 0.2 + 0.2 = 0.22.
So the square root of 0.05 is approximately 0.22
Common Mistakes and How to Avoid Them in the Square Root of 0.05
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few common 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 typically consider only the positive square root for practical purposes.
For example, √0.05 ≈ ±0.2236.
Square Root of 0.05 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.01?
The area of the square is 0.01 square units.
Explanation
The area of the square = side2.
The side length is given as √0.01.
Area of the square = (√0.01) x (√0.01)
= 0.1 x 0.1 = 0.01
Therefore, the area of the square box is 0.01 square units.
Problem 2
A square-shaped field measuring 0.05 square meters is built; if each of the sides is √0.05, what will be the square meters of half of the field?
0.025 square meters
Explanation
The given area is 0.05 square meters.
Dividing 0.05 by 2 gives us 0.025.
So, half of the field measures 0.025 square meters.
Problem 3
Calculate √0.05 x 10.
2.236
Explanation
First, find the square root of 0.05, which is approximately 0.2236.
Then multiply 0.2236 by 10. 0.2236 x 10 = 2.236
Problem 4
What will be the square root of (0.04 + 0.01)?
The square root is 0.2236
Explanation
To find the square root, sum (0.04 + 0.01) = 0.05
Then, √0.05 ≈ 0.2236
Therefore, the square root of (0.04 + 0.01) is ±0.2236
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √0.04 units and the width ‘w’ is 0.038 units.
We find the perimeter of the rectangle as 0.476 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√0.04 + 0.038)
= 2 × (0.2 + 0.038)
= 2 × 0.238
= 0.476 units.
FAQ on Square Root of 0.05
1.What is √0.05 in its simplest form?
2.Mention the factors of 0.05.
3.Calculate the square of 0.05.
4.Is 0.05 a prime number?
5.0.05 is divisible by?
Important Glossaries for the Square Root of 0.05
- Square root: A square root is the inverse of a square. For example, 0.22 = 0.04, and the inverse of the square is the square root, that is, √0.04 = 0.2.
- Irrational number: An irrational number is one that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Decimal: A decimal is a number that has a whole number and a fractional part separated by a decimal point, such as 0.05.
- Radical form: Expressing a number under a square root symbol, such as √0.05, is called radical form.
- Exponential form: Expressing a number with a fractional exponent, such as (0.05)(1/2), is called exponential form.
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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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