Square Root of 12/3
2026-02-28 06:13 Diff
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Last updated on August 5, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 12/3.

What is the Square Root of 12/3?

The square root is the inverse of the square of the number. 12/3 simplifies to 4, which is a perfect square. The square root of 12/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(12/3) = √4, whereas in the exponential form it is (4)^(1/2). √4 = 2, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 12/3

Since 12/3 simplifies to 4, which is a perfect square, we can use the prime factorization method to find the square root. However, for non-perfect squares, methods such as the long division method and approximation method can be used. Below are the methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 12/3 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 4 is broken down into its prime factors.

Step 1: Finding the prime factors of 4 Breaking it down, we get 2 x 2.

Step 2: Since 4 is a perfect square, we can group the factors in pairs. Thus, the square root of 4 can be found as √(2 x 2) = 2.

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Square Root of 12/3 by Long Division Method

The long division method is typically used for non-perfect square numbers, but it can also apply to perfect squares like 4 to verify results. Here’s how it works for √4:

Step 1: For 4, consider the closest perfect square less than or equal to 4, which is 4 itself.

Step 2: The square of 2 is 4, so 2 is our divisor, and the quotient is also 2.

Step 3: Subtract 4 from 4, resulting in a remainder of zero. Thus, the square root of √4 is 2.

Square Root of 12/3 by Approximation Method

The approximation method is generally used for non-perfect squares, but for educational purposes, it can apply here to verify results.

Step 1: Considering √4, we know it lies between the perfect squares of 1 (1^2) and 4 (2^2).

Step 2: Since 4 is exactly a perfect square, √4 = 2.

Common Mistakes and How to Avoid Them in the Square Root of 12/3

Students may make mistakes while finding the square root, like forgetting about the negative square root or misapplying methods. Here are some common errors:

Problem 1

Can you help Max find the area of a square box if its side length is given as √(12/3)?

Okay, lets begin

The area of the square is 4 square units.

Explanation

The area of the square = side^2.

The side length is given as √(12/3) = √4 = 2.

Area of the square = side^2 = 2 x 2 = 4.

Therefore, the area of the square box is 4 square units.

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Problem 2

A square-shaped building measuring 12/3 square feet is built; if each of the sides is √(12/3), what will be the square feet of half of the building?

Okay, lets begin

2 square feet

Explanation

The area of the building is 12/3 or 4, as the building is square-shaped.

Dividing 4 by 2 = 2. So half of the building measures 2 square feet.

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Problem 3

Calculate √(12/3) x 5.

Okay, lets begin

10

Explanation

The first step is to find the square root of 12/3, which is √4 = 2.

The next step is to multiply 2 by 5.

So 2 x 5 = 10.

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Problem 4

What will be the square root of (12/3 + 6)?

Okay, lets begin

The square root is √10.

Explanation

To find the square root, first calculate the sum of (12/3 + 6). 12/3 simplifies to 4, and 4 + 6 = 10.

The square root of 10 is approximately ±3.162.

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Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(12/3) units and the width ‘w’ is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as 10 units.

Explanation

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

Perimeter = 2 × (√4 + 3) = 2 × (2 + 3) = 2 × 5 = 10 units.

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FAQ on Square Root of 12/3

1.What is √(12/3) in its simplest form?

The prime factorization of 4 is 2 x 2, so the simplest form of √(12/3) = √4 = 2.

2.Mention the factors of 12/3.

12/3 simplifies to 4. Factors of 4 are 1, 2, and 4.

3.Calculate the square of 12/3.

We get the square of 12/3 by squaring the simplified number, that is 4 x 4 = 16.

4.Is 12/3 a prime number?

12/3 simplifies to 4, which is not a prime number, as it has more than two factors.

5.12/3 is divisible by?

12/3 simplifies to 4, which is divisible by 1, 2, and 4.

Important Glossaries for the Square Root of 12/3

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4.
  • Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 4, 9, and 16 are perfect squares.
  • Prime factorization: Prime factorization is the process of expressing a number as the product of its prime numbers.
  • Approximation: Approximation involves finding a value close to the exact answer. For example, the square root of 10 is approximately 3.162.

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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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: He loves to play the quiz with kids through algebra to make kids love it.