Last updated on May 26th, 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.
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.
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
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.
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.
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.
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.
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.
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.
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
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.
Calculate √(2/5) x 10.
6.32455
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.
What will be the square root of (2/5 + 1/10)?
The square root is approximately 0.707107.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(2/5) + 5)
≈ 2 × (0.632455 + 5).
Perimeter ≈ 2 × 5.632455
= 11.26491 units.
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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