Square Root of 2/5
2026-02-28 06:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2/5

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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as mathematics, physics, and engineering. Here, we will discuss the square root of 2/5.

What is the Square Root of 2/5?

The square root is the inverse of the square of a number. The fraction 2/5 is not a perfect square. The square root of 2/5 can be expressed in both radical and exponential form. In radical form, it is expressed as √(2/5), whereas (2/5)^(1/2) in exponential form. The square root of 2/5 is approximately 0.632455, which is an irrational number because it cannot be expressed as a ratio of two integers.

Finding the Square Root of 2/5

Square Root of 2/5 by Simplifying the Fraction

To simplify the process, let's understand how to handle the square root of a fraction. If we have √(a/b), we can separate this into √a/√b. Now, let's apply this to 2/5.

Step 1: Separate the fraction as √2/√5

Step 2: Calculate the square root of the numerator and the denominator. √2 ≈ 1.414 and √5 ≈ 2.236

Step 3: Divide the square root of the numerator by the square root of the denominator. So √(2/5) ≈ 1.414/2.236 ≈ 0.632455

Therefore, the square root of 2/5 is approximately 0.632455.

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Square Root of 2/5 by Long Division Method

The long division method is a systematic way to find the square root of non-perfect square numbers, including decimals. Let's see how to find the square root using this method, step by step.

Step 1: Convert 2/5 into a decimal, which is 0.4.

Step 2: Use the long division method to find the square root of 0.4.

Step 3: Pair the digits of 0.4 from the decimal point, so we have 40.

Step 4: Find a number whose square is less than or equal to 40. Let's take 6, as 6*6 = 36.

Step 5: Subtract 36 from 40, bringing down pairs of zeros to continue the process.

Step 6: Repeat the process to find subsequent digits until the desired accuracy is reached.

The approximate value of √0.4 is 0.632455.

Square Root of 2/5 by Approximation Method

The approximation method is another way to find the square roots and is a straightforward method to find the square root of a given number. Let us learn how to find the square root of 2/5 using the approximation method.

Step 1: Convert 2/5 into a decimal, which is 0.4.

Step 2: Identify two perfect squares between which 0.4 lies. It lies between 0.36 (0.6^2) and 0.49 (0.7^2).

Step 3: Use interpolation to approximate the square root. Since 0.4 is closer to 0.36, we can start with an initial guess of 0.63.

Step 4: Refine the approximation by checking the squares of values around the initial guess until the desired precision is achieved.

Thus, the square root of 0.4 is approximately 0.632455.

Common Mistakes and How to Avoid Them in the Square Root of 2/5

Students may make mistakes while finding the square root, such as neglecting the importance of the negative square root or misapplying methods. Let us look at a few common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(2/5)?

Okay, lets begin

The area of the square is approximately 0.4 square units.

Explanation

The area of the square = side^2.

The side length is given as √(2/5).

Area of the square = (√(2/5))^2

= 2/5

= 0.4.

Therefore, the area of the square box is 0.4 square units.

Well explained 👍

Problem 2

A square-shaped garden measuring 2/5 square meters is built. If each of the sides is √(2/5), what will be the square meters of half of the garden?

Okay, lets begin

0.2 square meters

Explanation

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

Dividing 2/5 (0.4) by 2 gives us 0.2.

So half of the garden measures 0.2 square meters.

Well explained 👍

Problem 3

Calculate √(2/5) x 10.

Okay, lets begin

6.32455

Explanation

The first step is to find the square root of 2/5, which is approximately 0.632455.

The second step is to multiply 0.632455 by 10.

So, 0.632455 x 10 = 6.32455.

Well explained 👍

Problem 4

What will be the square root of (2/5 + 1/10)?

Okay, lets begin

The square root is approximately 0.707107.

Explanation

To find the square root, first find the sum of (2/5 + 1/10).

2/5 = 4/10,

so 4/10 + 1/10

= 5/10

= 1/2.

Therefore, √(1/2) = ±√0.5

≈ ±0.707107.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(2/5) units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is approximately 11.26491 units.

Explanation

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

Perimeter = 2 × (√(2/5) + 5)

≈ 2 × (0.632455 + 5).

Perimeter ≈ 2 × 5.632455

= 11.26491 units.

Well explained 👍

FAQ on Square Root of 2/5

1.What is √(2/5) in its simplest form?

The simplest form of √(2/5) is √2/√5. Since neither number is a perfect square, the simplest radical form is √2/√5.

2.What are the factors of 2/5?

The fraction 2/5 consists of the factors: numerator 2 (factors are 1 and 2) and denominator 5 (factors are 1 and 5).

3.Calculate the square of 2/5.

The square of 2/5 is found by multiplying the fraction by itself: (2/5) x (2/5) = 4/25 = 0.16.

4.Is 2/5 a rational number?

Yes, 2/5 is a rational number because it can be expressed as a ratio of two integers, 2 and 5, with the denominator not equal to zero.

5.Is 2/5 divisible by 2?

No, 2/5 as a fraction is not divisible by 2, since 5 is not a factor of 2.

Instead, 2/5 can be divided as a fraction by multiplying the reciprocal of 2.

Important Glossaries for the Square Root of 2/5

  • Square root: The square root is the number that, when multiplied by itself, gives the original number. Example: √(2/5) ≈ 0.632455.
     
  • Rational number: A rational number can be expressed as a fraction of two integers, where the denominator is not zero.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction; its decimal representation is non-repeating and non-terminating.
     
  • Decimal: A number that consists of a whole number and a fractional part separated by a decimal point. For example, 0.632455 is a decimal.
     
  • Fraction: A fraction represents a part of a whole or any number of equal parts, expressed as a/b, where 'a' is the numerator and 'b' is the denominator.

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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.