Last updated on May 26th, 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 2/7.
The square root is the inverse of the square of the number. 2/7 is not a perfect square. The square root of 2/7 can be expressed in both radical and exponential forms. In radical form, it is expressed as √(2/7), whereas in exponential form, it is expressed as (2/7)^(1/2). The square root of 2/7 is approximately 0.53452, 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.
The prime factorization method is typically used for perfect squares. However, for non-perfect squares like 2/7, methods such as the long-division method and approximation method are used. Let us now learn these methods:
The product of prime factors is the prime factorization of a number. Since 2/7 is a fraction, we don't use prime factorization in the traditional sense. Instead, we consider the prime factors of the numerator and the denominator separately:
Step 1: The prime factors of 2 are just 2 itself, and 7 is a prime number.
Step 2: Since 2/7 is not a perfect square, we can't pair the prime factors in the usual way.
Therefore, calculating the square root of 2/7 using prime factorization alone is not feasible.
The long division method is particularly useful for non-perfect square numbers. Here is how to find the square root using the long division method, step by step:
Step 1: To find the square root of a fraction, consider the square roots of the numerator and denominator separately.
Step 2: Find √2 using long division, which is approximately 1.414.
Step 3: Find √7 using long division, which is approximately 2.646.
Step 4: Divide √2 by √7 to get the square root of 2/7: 1.414/2.646 ≈ 0.53452.
The approximation method is another approach to finding square roots and is a straightforward way to find the square root of a given number. Here is how to find the square root of 2/7 using this method:
Step 1: Identify the approximate values of √2 and √7. We know that √2 ≈ 1.414 and √7 ≈ 2.646.
Step 2: Divide these approximate values: 1.414/2.646 ≈ 0.53452.
Step 3: This value is the approximate square root of 2/7.
Students often make mistakes when finding the square root, such as forgetting about the negative square root, skipping steps in methods, etc. Let's look at some common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √(2/7)?
The area of the square is approximately 0.2857 square units.
The area of the square = side².
The side length is given as √(2/7).
Area of the square = (√(2/7))²
= 2/7
≈ 0.2857.
Therefore, the area of the square box is approximately 0.2857 square units.
A square-shaped building measuring 2/7 square meters is built; if each of the sides is √(2/7), what will be the square meters of half of the building?
0.1429 square meters
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2/7 by 2, we get 1/7 ≈ 0.1429.
So half of the building measures approximately 0.1429 square meters.
Calculate √(2/7) x 5.
Approximately 2.6726
The first step is to find the square root of 2/7, which is approximately 0.53452.
The second step is to multiply 0.53452 by 5.
So, 0.53452 x 5 ≈ 2.6726.
What will be the square root of (2/7 + 1)?
Approximately 1.1832
To find the square root, we need to find the sum of (2/7 + 1). 2/7 + 1 = 9/7 ≈ 1.2857, and then √(9/7) ≈ 1.1832.
Therefore, the square root of (2/7 + 1) is approximately ±1.1832.
Find the perimeter of the rectangle if its length 'l' is √(2/7) units and the width 'w' is 3 units.
We find the perimeter of the rectangle as approximately 7.069 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(2/7) + 3)
= 2 × (0.53452 + 3)
≈ 2 × 3.53452
≈ 7.069 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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