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 vehicle design, finance, etc. Here, we will discuss the square root of 1/2.
The square root is the inverse of the square of the number. 1/2 is not a perfect square. The square root of 1/2 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/2), whereas (1/2)^(1/2) in the exponential form. √(1/2) = 0.70710678118, 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 used for perfect square numbers. However, for non-perfect square numbers like 1/2, methods such as the long-division method and approximation method are used. Let us now learn the following methods:
The prime factorization method involves expressing a number as the product of prime factors.
Since 1/2 is a fraction and not a whole number, traditional prime factorization is not applicable.
Therefore, calculating 1/2 using prime factorization is not feasible.
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:
Step 1: To begin with, convert 1/2 to a decimal, which is 0.5.
Step 2: Find the closest perfect square numbers around 0.5. The closest are 0.25 (0.5 squared) and 1.
Step 3: Apply the long division method to approximate the square root of 0.5.
Step 4: Continue the division until the desired decimal place accuracy is reached. After following these steps, the square root of 0.5 is approximately 0.70710678118.
Approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1/2 using the approximation method.
Step 1: Convert 1/2 to a decimal, which is 0.5.
Step 2: Identify the closest perfect squares around 0.5, which are 0.25 and 1.
Step 3: Use linear interpolation to approximate the square root, calculating the position of 0.5 between 0.25 and 1.
Using this method, we find that √(0.5) ≈ 0.7071.
Students often make mistakes while finding square roots, such as ignoring negative roots or misapplying methods. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √(1/2)?
The area of the square is 0.5 square units.
The area of the square = side².
The side length is given as √(1/2).
Area of the square = (√(1/2))² = 1/2 = 0.5.
A square-shaped building measuring 1/2 square feet is built; if each of the sides is √(1/2), what will be the square feet of half of the building?
0.25 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1/2 by 2 = we get 0.25.
Calculate √(1/2) x 5.
3.5355339059
The first step is to find the square root of 1/2, which is approximately 0.7071.
The second step is to multiply 0.7071 with 5.
So 0.7071 x 5 = 3.5355339059.
What will be the square root of (0.5 + 0.5)?
The square root is 1.
To find the square root, we need to find the sum of (0.5 + 0.5). 0.5 + 0.5 = 1, and then √1 = 1.
Therefore, the square root of (0.5 + 0.5) is ±1.
Find the perimeter of a rectangle if its length ‘l’ is √(1/2) units and the width ‘w’ is 2 units.
We find the perimeter of the rectangle as 5.414213562 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(1/2) + 2) = 2 × (0.7071 + 2) = 2 × 2.7071 = 5.414213562 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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