106 LearnersLast updated on May 26th, 2025
Square Root of 2/5
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
The prime factorization method is not applicable to non-integers. For fractions, we can find the square root by finding the square root of the numerator and the denominator separately. Let us now learn the following methods: Simplifying the fraction Finding square roots of numerator and denominator
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.
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.
Mistake 1
Forgetting about the negative square root
It is important to remind students that every positive number has both positive and negative square roots. However, we usually consider only the principal (positive) square root for calculations unless specified otherwise.
For example, √(2/5) = ±0.632455.
Mistake 2
Incorrectly simplifying fractions under a square root
A common mistake is to simplify fractions incorrectly under a square root. To avoid this, teach students to separate the square root of a fraction into the square root of the numerator and the square root of the denominator.
For example: √(2/5) = √2/√5.
Mistake 3
Not finding the correct value of a non-perfect square
Students may err by rounding too early or inaccurately when dealing with non-perfect squares. Emphasize the importance of using sufficient decimal places for accurate results.
For example, √0.4 = 0.632455, not 0.63.
Mistake 4
Confusing the square root symbol with the cube root
Students need to differentiate between square root and cube root symbols.
For example, √(2/5) and ∛(2/5) are different operations. Regular practice can help avoid this confusion.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves several steps. Students may skip steps accidentally, leading to incorrect answers. Encourage careful, step-by-step calculation to ensure accuracy.
Square Root of 2/5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(2/5)?
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.
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?
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.
Problem 3
Calculate √(2/5) x 10.
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.
Problem 4
What will be the square root of (2/5 + 1/10)?
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.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(2/5) units and the width ‘w’ is 5 units.
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.
FAQ on Square Root of 2/5
1.What is √(2/5) in its simplest form?
2.What are the factors of 2/5?
3.Calculate the square of 2/5.
4.Is 2/5 a rational number?
5.Is 2/5 divisible by 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.
