Square Root of 0.2
2026-02-28 09:07 Diff
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Last updated on August 5, 2025

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 like vehicle design, finance, etc. Here, we will discuss the square root of 0.2.

What is the Square Root of 0.2?

The square root is the inverse of the square of the number. 0.2 is not a perfect square. The square root of 0.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.2, whereas (0.2)^(1/2) in the exponential form. √0.2 ≈ 0.44721, 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 0.2

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 0.2, methods like long-division and approximation are used. Let us now learn the following methods: - Long division method - Approximation method

Square Root of 0.2 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: To begin with, we need to group the digits of 0.2 as 0.20.

Step 2: Find a number whose square is less than or equal to 0. The closest is 0, so the quotient starts with 0.

Step 3: Bring down the next pair of digits, which is 20, making it 0.20.

Step 4: Double the quotient and use it as the new divisor. Double of 0 is 0.

Step 5: Find a number n such that (0n) × n ≤ 20. The closest is 4, as 04 × 4 = 16.

Step 6: Subtract 16 from 20 to get 4, and add a decimal point to continue division.

Step 7: Bring down two zeroes to make it 400.

Step 8: Double the current quotient 0.4 to get 0.8 as the next divisor.

Step 9: Find a number n such that (0.8n) × n ≤ 400. Here, n would be 5 as 0.85 × 5 = 425, which is too large, so we use 0.84 × 4 = 336. Continue the process until sufficient decimal places are found.

So the square root of √0.2 ≈ 0.44721.

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Square Root of 0.2 by Approximation Method

The approximation method is another method for finding square roots. It's an easy way to find the square root of a given number. Now let us learn how to find the square root of 0.2 using the approximation method.

Step 1: Find the closest perfect squares around 0.2. The perfect square less than 0.2 is 0.16 (which is 0.4²), and the perfect square greater than 0.2 is 0.25 (which is 0.5²). √0.2 falls between 0.4 and 0.5.

Step 2: Apply the formula (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula (0.2 - 0.16) / (0.25 - 0.16) = 0.04 / 0.09 ≈ 0.4444. Add this to 0.4, so the square root of 0.2 is approximately 0.4444, which aligns with our earlier long division result of approximately 0.44721.

Common Mistakes and How to Avoid Them in the Square Root of 0.2

Students often make mistakes while finding square roots, such as forgetting the negative square root or skipping steps in the long division method. Let's look at some mistakes students tend to make in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √0.2?

Okay, lets begin

The area of the square is approximately 0.2 square units.

Explanation

The area of the square = side².

The side length is given as √0.2.

Area of the square = side²

= (√0.2) × (√0.2)

= 0.2.

Therefore, the area of the square box is approximately 0.2 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 0.2 square feet is built; if each of the sides is √0.2, what will be the area of half of the building?

Okay, lets begin

0.1 square feet.

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 0.2 by 2 = 0.1.

So half of the building measures 0.1 square feet.

Well explained 👍

Problem 3

Calculate √0.2 × 5.

Okay, lets begin

Approximately 2.23605.

Explanation

The first step is to find the square root of 0.2 which is approximately 0.44721, then multiply 0.44721 with 5.

So, 0.44721 × 5 ≈ 2.23605.

Well explained 👍

Problem 4

What will be the square root of (0.2 + 0.05)?

Okay, lets begin

The square root is approximately 0.5.

Explanation

To find the square root, first calculate the sum of (0.2 + 0.05). 0.2 + 0.05 = 0.25, then √0.25 = 0.5. Therefore, the square root of (0.2 + 0.05) is ±0.5.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √0.2 units and the width ‘w’ is 1 unit.

Okay, lets begin

The perimeter of the rectangle is approximately 2.89442 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√0.2 + 1)

= 2 × (0.44721 + 1)

≈ 2 × 1.44721

= 2.89442 units.

Well explained 👍

FAQ on Square Root of 0.2

1.What is √0.2 in its simplest form?

The square root of 0.2 is approximately 0.44721, which cannot be simplified further as it is an irrational number.

2.What are the factors of 0.2?

Factors of 0.2 as a decimal number are 1, 0.2, 0.1, and 0.05.

3.Calculate the square of 0.2.

The square of 0.2 is found by multiplying 0.2 by itself, that is 0.2 × 0.2 = 0.04.

4.Is 0.2 a prime number?

5.What numbers can 0.2 be divided by?

0.2 can be divided by 1, 0.2, 0.1, and 0.05.

Important Glossaries for the Square Root of 0.2

  • Square root: A square root is the inverse of squaring a number. For example, if 4² = 16, then √16 = 4.
     
  • Irrational number: An irrational number cannot be written as a simple fraction; it has non-repeating, non-terminating decimals. For example, √2 is irrational.
     
  • Decimal: A decimal is a number that includes a whole number and a fractional part separated by a decimal point, such as 0.2.
     
  • Approximation: The method of finding a value that is close enough to the right answer, usually with a specified degree of accuracy.
     
  • Long division: A method for dividing large numbers by breaking the division process into a series of easier steps.

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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

: He loves to play the quiz with kids through algebra to make kids love it.