Square Root of 0.03
2026-02-28 12:57 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-0.03

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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 0.03

What is the Square Root of 0.03?

The square root is the inverse of the square of the number. 0.03 is not a perfect square. The square root of 0.03 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.03, whereas (0.03)^(1/2) is in the exponential form. √0.03 ≈ 0.1732, 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 0.03

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 method and approximation method are used. Let us now learn the following methods:

  • Long division method
  • Approximation method

Square Root of 0.03 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, express 0.03 as 3/100.

Step 2: Use the long division technique to find the square root of 3. Group the digits of 3 as 03, and add pairs of zeros after the decimal point to continue the division.

Step 3: Find a number whose square is less than or equal to 3. The closest number is 1, since 1 * 1 = 1. Subtract and bring down the next pair of digits (00), making it 200.

Step 4: Double the quotient obtained so far (1), making it 2, and find a digit x such that 2x * x is less than or equal to 200. The digit x is 7, because 27 * 7 = 189. Subtract 189 from 200 to get 11, and bring down the next pair of zeros, making it 1100.

Step 5: Repeat this process to get more decimal places if needed. The result is approximately 1.732.

Step 6: Since we are finding the square root of 0.03, divide 1.732 by 10 to adjust for the original factor of 1/100.

Thus, √0.03 ≈ 0.1732.

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Square Root of 0.03 by Approximation Method

The approximation method is another method for finding the square roots, and 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 0.03 using the approximation method.

Step 1: Identify the perfect squares surrounding 0.03. The smallest perfect square less than 0.03 is 0.01 (√0.01 = 0.1), and the closest greater perfect square is 0.04 (√0.04 = 0.2).

Step 2: Since 0.03 lies between 0.01 and 0.04, the square root of 0.03 lies between 0.1 and 0.2.

Step 3: Use interpolation to approximate further. (0.03 - 0.01) / (0.04 - 0.01) gives us 2/3 of the way between 0.1 and 0.2, which is approximately 0.1732.

Therefore, the square root of 0.03 is approximately 0.1732.

Common Mistakes and How to Avoid Them in the Square Root of 0.03

Students make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods. Now let us look at a few of those mistakes that 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 √0.07?

Okay, lets begin

The area of the square is approximately 0.07 square units.

Explanation

The area of the square = side².

The side length is given as √0.07.

Area of the square = side²

= √0.07 * √0.07

≈ 0.2646 * 0.2646

≈ 0.07.

Therefore, the area of the square box is approximately 0.07 square units.

Well explained 👍

Problem 2

A square-shaped plot measuring 0.03 square meters is built; if each of the sides is √0.03, what will be the square meters of half of the plot?

Okay, lets begin

0.015 square meters

Explanation

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

Dividing 0.03 by 2 gives us 0.015.

So half of the plot measures 0.015 square meters.

Well explained 👍

Problem 3

Calculate √0.03 x 5.

Okay, lets begin

0.866

Explanation

The first step is to find the square root of 0.03, which is approximately 0.1732.

The second step is to multiply 0.1732 by 5.

So 0.1732 x 5 ≈ 0.866.

Well explained 👍

Problem 4

What will be the square root of (0.02 + 0.01)?

Okay, lets begin

The square root is approximately 0.1732.

Explanation

To find the square root, we need to find the sum of (0.02 + 0.01). 0.02 + 0.01 = 0.03, and then √0.03 ≈ 0.1732.

Therefore, the square root of (0.02 + 0.01) is approximately ±0.1732.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √0.07 units and the width ‘w’ is 0.05 units.

Okay, lets begin

The perimeter of the rectangle is approximately 0.628 units.

Explanation

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

Perimeter = 2 × (√0.07 + 0.05)

= 2 × (0.2646 + 0.05)

≈ 2 × 0.3146

≈ 0.628 units.

Well explained 👍

FAQ on Square Root of 0.03

1.What is √0.03 in its simplest form?

The simplest form of √0.03 is √(3/100) = √3/10 ≈ 0.1732.

2.Mention the factors of 0.03.

Factors of 0.03 include 1, 0.01, 0.03, 0.1, 0.3, and 3.

3.Calculate the square of 0.03.

We get the square of 0.03 by multiplying the number by itself, that is 0.03 x 0.03 = 0.0009.

4.Is 0.03 a prime number?

5.0.03 is divisible by?

0.03 is divisible by 0.01, 0.03, and 1, among others.

Important Glossaries for the Square Root of 0.03

  • Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 0.1732, 0.5, and 0.75 are decimals.
     
  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into pairs and finding successive quotients.
     
  • Approximation method: A technique used to estimate the square root of a number by identifying nearby perfect squares and interpolating between them.

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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.