Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. Square roots are widely used in fields such as design and finance. Here, we will discuss the square root of 3/3.
The square root is the inverse of squaring a number. Since 3/3 simplifies to 1, which is a perfect square, the square root of 3/3 is 1. It can be expressed in both radical and exponential form. In radical form, it is expressed as √(3/3), which simplifies to √1. In exponential form, it is (3/3)^(1/2), which simplifies to 1. The square root of 3/3 is 1, a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Since 3/3 simplifies to 1, and 1 is a perfect square, finding its square root is straightforward. We can use basic multiplication properties or prime factorization to confirm the result:
The prime factorization of 1 is trivial since 1 is itself and has no prime factors. Therefore, there is no need for pairing or further calculations. The square root of 1, and thus 3/3, is simply 1.
Since 3/3 simplifies to 1, and 1 times 1 equals 1, the square root of 3/3 is 1.
This method directly shows that multiplying 1 by itself gives the original number.
While discussing the square root of fractions, it is important to simplify the fraction first.
Here, 3/3 equals 1, and the square root of 1 is straightforwardly 1.
Avoid over-complicating the process by not simplifying the fraction first.
Students may make errors when simplifying fractions before taking the square root, or they may confuse properties of square roots with those of other roots.
Let's explore some common mistakes and their solutions.
Can you help Max find the area of a square box if its side length is given as √(3/3)?
The area of the square is 1 square unit.
The area of the square = side².
The side length is given as √(3/3), which simplifies to 1.
Area of the square = side² = 1 x 1 = 1.
Therefore, the area of the square box is 1 square unit.
A square-shaped building measuring 3/3 square feet is built; if each of the sides is √(3/3), what will be the square feet of half of the building?
0.5 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1 by 2, we get 0.5.
So half of the building measures 0.5 square feet.
Calculate √(3/3) x 5.
5
The first step is to find the square root of 3/3, which is 1.
The second step is to multiply 1 with 5.
So 1 x 5 = 5.
What will be the square root of (3/3 + 1)?
The square root is √2.
To find the square root, we need to find the sum of (3/3 + 1). 3/3 + 1 = 1 + 1 = 2, and then √2 is the result.
Therefore, the square root of (3/3 + 1) is ±√2.
Find the perimeter of the rectangle if its length ‘l’ is √(3/3) units and the width ‘w’ is 2 units.
We find the perimeter of the rectangle as 6 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(3/3) + 2) = 2 × (1 + 2) = 2 × 3 = 6 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.
: He loves to play the quiz with kids through algebra to make kids love it.