Square Root of 0.0008
2026-02-28 17:15 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-0.0008

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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. Square roots are used in fields like engineering, finance, and more. Here, we will discuss the square root of 0.0008.

What is the Square Root of 0.0008?

The square root is the inverse operation of squaring a number. Since 0.0008 is not a perfect square, its square root can be expressed in radical and exponential forms. In radical form, it is √0.0008, and in exponential form, it is (0.0008)^(1/2). The square root of 0.0008 is approximately 0.028284, which is an irrational number because it cannot be expressed as a simple fraction.

Finding the Square Root of 0.0008

For perfect squares, the prime factorization method is used, but for non-perfect squares like 0.0008, methods such as long division and approximation are more appropriate.

Let's explore these methods: 

  • Long division method
  • Approximation method

Square Root of 0.0008 by Long Division Method

The long division method is useful for non-perfect squares. Here's how to find the square root of a number using this method:

Step 1: Start by pairing digits from right to left. For 0.0008, group as 08.

Step 2: Determine the largest number whose square is less than or equal to 8. Here, 2 works because 2² = 4. The quotient is 2, and the remainder is 8 - 4 = 4.

Step 3: Bring down two zeros, making the new dividend 400. Double the quotient (2), giving us 4.

Step 4: Find n such that (4n) × n ≤ 400. If n = 7, (47) × 7 = 329.

Step 5: Subtract 329 from 400, leaving 71.

Step 6: Add two zeros to make it 7100 and repeat the process until you achieve the desired precision.

The square root of 0.0008 is approximately 0.028284.

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Square Root of 0.0008 by Approximation Method

The approximation method provides a straightforward way to find square roots. Here's how to approximate the square root of 0.0008:

Step 1: Identify the perfect squares closest to 0.0008. The closest are 0.0004 (0.02²) and 0.0016 (0.04²). Thus, √0.0008 is between 0.02 and 0.04.

Step 2: Use interpolation: (Number - Lower perfect square) / (Upper perfect square - Lower perfect square). For example: (0.0008 - 0.0004) / (0.0016 - 0.0004) = 0.4 / 1.2 = 0.3333.

Step 3: Add this to the lower bound: 0.02 + 0.3333(0.02) = 0.026666.

Refining further yields an approximation of 0.028284.

Common Mistakes and How to Avoid Them in Finding the Square Root of 0.0008

Mistakes occur when calculating square roots, such as forgetting negative roots or misusing the long division method. Here are some mistakes and tips to avoid them:

Problem 1

Can you help Max find the area of a square box if its side length is √0.0005?

Okay, lets begin

The area of the square is 0.0005 square units.

Explanation

The area of the square = side².

The side length is given as √0.0005.

Area of the square = side² = √0.0005 × √0.0005

= 0.02236 × 0.02236 = 0.0005

Therefore, the area of the square box is 0.0005 square units.

Well explained 👍

Problem 2

A square-shaped sheet measuring 0.0008 square meters is cut; if each of the sides is √0.0008, what will be the square meters of half of the sheet?

Okay, lets begin

0.0004 square meters

Explanation

Divide the given area by 2 since the sheet is square-shaped.

Dividing 0.0008 by 2 = 0.0004

So half of the sheet measures 0.0004 square meters.

Well explained 👍

Problem 3

Calculate √0.0008 × 5.

Okay, lets begin

0.14142

Explanation

First, find the square root of 0.0008, which is approximately 0.028284.

Then multiply 0.028284 by 5. So, 0.028284 × 5 = 0.14142

Well explained 👍

Problem 4

What will be the square root of (0.0005 + 0.0003)?

Okay, lets begin

The square root is approximately 0.028284.

Explanation

Find the sum of 0.0005 + 0.0003, which equals 0.0008.

The square root of 0.0008 is approximately 0.028284.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √0.0005 units and the width ‘w’ is 0.01 units.

Okay, lets begin

The perimeter of the rectangle is approximately 0.06472 units.

Explanation

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

Perimeter = 2 × (√0.0005 + 0.01)

= 2 × (0.02236 + 0.01)

= 2 × 0.03236

= 0.06472 units.

Well explained 👍

FAQ on Square Root of 0.0008

1.What is √0.0008 in its simplest form?

The number 0.0008 can be expressed as 8 x 10^(-4).

The simplest form of √0.0008 = √(8 x 10^(-4)).

2.What are the factors of 0.0008?

Factors of 0.0008 include 1, 2, 4, 8, 0.1, 0.2, 0.4, and 0.8.

3.Calculate the square of 0.0008.

To find the square of 0.0008, multiply it by itself: 0.0008 × 0.0008 = 0.00000064.

4.Is 0.0008 a rational number?

Yes, 0.0008 is a rational number because it can be expressed as a fraction (8/10000).

5.Is 0.0008 divisible by 0.2?

No, 0.0008 is not divisible by 0.2 because 0.0008 ÷ 0.2 is not an integer.

Important Glossaries for the Square Root of 0.0008

  • Square root: The square root is the inverse operation of squaring a number. For example, 4² = 16, so √16 = 4.
     
  • Irrational number: A number that cannot be expressed as a simple fraction, such as the square root of a non-perfect square.
     
  • Approximation: The process of finding a value close to the actual value. For example, √0.0008 ≈ 0.028284.
     
  • Decimal: A numerical value with a fractional part, represented with a dot, such as 0.03, 0.25.
     
  • Long division method: A technique used to find the square root of non-perfect squares through successive approximations.

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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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