126 LearnersLast updated on May 26th, 2025
Square Root of 3/7
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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3/7.
What is the Square Root of 3/7?
The square root is the inverse of the square of a number. The fraction 3/7 is not a perfect square. The square root of 3/7 can be expressed in both radical and exponential form. In the radical form, it is expressed as √(3/7), whereas in the exponential form, it is (3/7)^(1/2). The square root of 3/7 is approximately 0.65465, 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.
Finding the Square Root of 3/7
For non-perfect squares, methods such as the long division method and approximation method are used to find square roots. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 3/7 by Long Division Method
The long division method is particularly used for non-perfect squares. In this method, we can find the square root of a fraction by finding the square roots of the numerator and denominator separately.
Step 1: Find the square root of the numerator 3 and the denominator 7 separately using the long division method.
Step 2: The approximate square root of 3 is 1.732, and the square root of 7 is 2.646.
Step 3: Divide the square root of the numerator by the square root of the denominator: 1.732 / 2.646 ≈ 0.65465.
So, the square root of 3/7 is approximately 0.65465.
Square Root of 3/7 by Approximation Method
The approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 3/7 using the approximation method.
Step 1: Estimate the square root of the numerator 3, which is between 1 and 2. Similarly, estimate the square root of the denominator 7, which is between 2 and 3.
Step 2: Use the approximation formula to adjust the estimates and divide them to get the square root of the fraction. By approximation, √3 ≈ 1.732 and √7 ≈ 2.646, so √(3/7) ≈ 0.65465.
Common Mistakes and How to Avoid Them in the Square Root of 3/7
Students often make mistakes while finding the square root, such as forgetting about the negative square root or failing to simplify fractions correctly. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we generally take only the positive square root in practical applications.
For example, √(3/7) = ±0.65465, but we typically use the positive value.
Mistake 2
Not simplifying the fraction before finding the square root
Some students forget to simplify the fraction before finding its square root. Always check if the fraction can be simplified to make calculations easier. Simplification should be done first to ensure accurate results.
Mistake 3
Not finding the correct value of a non-perfect square
It's crucial to accurately approximate the square roots of non-perfect squares to avoid errors.
For example, √3 ≈ 1.732 and √7 ≈ 2.646, not 2 or 3.
Mistake 4
Confusing the square root with the reciprocal
Students sometimes confuse finding the square root with finding the reciprocal. Ensure clarity by teaching the difference between square roots and reciprocals.
Mistake 5
Incorrect division during approximation
Errors can occur in the division step when approximating square roots. It is vital to perform division carefully to avoid incorrect results.
Square Root of 3/7 Examples
Problem 1
Can you help find the area of a square box if its side length is given as √(3/7)?
The area of the square is approximately 0.428 square units.
Explanation
The area of the square = side^2.
The side length is given as √(3/7).
Area of the square = (√(3/7))^2
= 3/7
≈ 0.428.
Therefore, the area of the square box is approximately 0.428 square units.
Problem 2
A square-shaped garden has an area of 3/7 square meters. If each of the sides is √(3/7), what will be the area of half of the garden?
0.214 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 3/7 by 2, we get 3/14 ≈ 0.214.
So half of the garden measures approximately 0.214 square meters.
Problem 3
Calculate √(3/7) x 5.
Approximately 3.27325
Explanation
First, find the square root of 3/7, which is approximately 0.65465.
Then multiply it by 5. So, 0.65465 x 5 ≈ 3.27325.
Problem 4
What will be the square root of (3/7 + 1)?
The square root is approximately 1.1547
Explanation
To find the square root, first find the sum of (3/7 + 1).
3/7 + 1 = 10/7.
Then √(10/7) ≈ 1.1547.
Therefore, the square root of (3/7 + 1) is approximately ±1.1547.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √(3/7) units and the width 'w' is 2 units.
The perimeter of the rectangle is approximately 5.3093 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(3/7) + 2)
≈ 2 × (0.65465 + 2)
= 2 × 2.65465
≈ 5.3093 units.
FAQ on Square Root of 3/7
1.What is √(3/7) in its simplest form?
2.How do you find the square root of a fraction?
3.Calculate the square of 3/7.
4.Is 3/7 a rational number?
5.3/7 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 3/7?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 3/7?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 3/7
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Fraction: A fraction represents a part of a whole and is expressed as p/q where p and q are integers and q ≠ 0.
- Rational number: A rational number can be expressed as a fraction where both the numerator and the denominator are integers.
- Approximation method: A technique used to find an estimated value of a square root, especially for non-perfect squares.
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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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