Square Root of 1/2
2026-02-28 06:16 Diff
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Last updated on August 5, 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.

What is 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.

Finding the Square Root of 1/2

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:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 1/2 by Prime Factorization Method

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.

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Square Root of 1/2 by Long Division Method

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.

Square Root of 1/2 by Approximation Method

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.

Common Mistakes and How to Avoid Them in the Square Root of 1/2

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/2)?

Okay, lets begin

The area of the square is 0.5 square units.

Explanation

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.

Well explained 👍

Problem 2

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?

Okay, lets begin

0.25 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 1/2 by 2 = we get 0.25.

Well explained 👍

Problem 3

Calculate √(1/2) x 5.

Okay, lets begin

3.5355339059

Explanation

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.

Well explained 👍

Problem 4

What will be the square root of (0.5 + 0.5)?

Okay, lets begin

The square root is 1.

Explanation

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(1/2) units and the width ‘w’ is 2 units.

Okay, lets begin

We find the perimeter of the rectangle as 5.414213562 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√(1/2) + 2) = 2 × (0.7071 + 2) = 2 × 2.7071 = 5.414213562 units.

Well explained 👍

FAQ on Square Root of 1/2

1.What is √(1/2) in its simplest form?

The simplest form of √(1/2) is √(1/2) itself, or approximately 0.7071.

2.Mention the factors of 1/2.

3.Calculate the square of 1/2.

We get the square of 1/2 by multiplying the number by itself, that is (1/2) × (1/2) = 1/4.

4.Is 1/2 a prime number?

1/2 is not a prime number; it's a fraction. Prime numbers are whole numbers greater than 1 with exactly two factors: 1 and themselves.

5.1/2 is divisible by?

1/2 can be expressed as a fraction and is divisible by 1 and 1/2 itself in the context of fractions.

Important Glossaries for the Square Root of 1/2

  • 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.
  • Principal square root: A number has both positive and negative square roots; however, it is usually the positive square root, known as the principal square root, that is used in real-world applications.
  • Fractions: A fraction represents a part of a whole, expressed as a numerator over a denominator, such as 1/2.
  • Decimals: A decimal is a number that uses a decimal point to show a fraction of a base-10 number, such as 0.5.

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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.