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Last updated on May 26th, 2025

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Square Root of 3/3

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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.

Square Root of 3/3 for Filipino Students
Professor Greenline from BrightChamps

What is 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.

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Finding the Square Root of 3/3

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:

 

  • Prime factorization method
  • Multiplication method
Professor Greenline from BrightChamps

Square Root of 3/3 by Prime Factorization Method

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.

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Square Root of 3/3 by Multiplication Method

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.

Professor Greenline from BrightChamps

Mistakes to Avoid with Square Root of 3/3

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.

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

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.

Mistake 1

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Forgetting to Simplify the Fraction

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Before finding the square root of a fraction, always simplify it.

Failing to simplify 3/3 to 1 will lead to incorrect results.

Always simplify the fraction first, then find the square root.

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Square Root of 3/3 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

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

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The area of the square is 1 square unit.

Explanation

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.

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Max, the Girl Character from BrightChamps

Problem 2

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?

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0.5 square feet

Explanation

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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(3/3) x 5.

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5

Explanation

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.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3/3 + 1)?

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The square root is √2.

Explanation

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.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(3/3) units and the width ‘w’ is 2 units.

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We find the perimeter of the rectangle as 6 units.

Explanation

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

Perimeter = 2 × (√(3/3) + 2) = 2 × (1 + 2) = 2 × 3 = 6 units.

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FAQ on Square Root of 3/3

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

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2.Is 3/3 a perfect square?

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3.Calculate the square of 3/3.

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4.Is 3/3 a rational number?

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5.What is the result of dividing 3 by 3?

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6.How does learning Algebra help students in Philippines make better decisions in daily life?

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7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 3/3?

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8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 3/3?

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9.Does learning Algebra support future career opportunities for students in Philippines?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3/3

  • Square root: The square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 1 is 1.

 

  • Rational number: A rational number can be expressed as a fraction of two integers. For example, 1 is a rational number as it can be expressed as 1/1.

 

  • Perfect square: A number that is the square of an integer. For example, 1 is a perfect square.

 

  • Fraction: A numerical quantity that is not a whole number, represented by two numbers divided by a slash. For example, 3/3 is a fraction.

 

  • Simplification: The process of reducing a fraction or expression to its simplest form. For example, 3/3 simplifies to 1.
Professor Greenline from BrightChamps

About BrightChamps in Philippines

At BrightChamps, we believe algebra is more than symbols—it’s a gateway to countless opportunities! Our mission is to support children across the Philippines in mastering key math skills, focusing today on the Square Root of 3/3 with an emphasis on understanding square roots—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy the latest gadgets, mastering algebra builds their confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different styles, we tailor our approach to each learner. From Manila’s busy streets to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting and relevant throughout the Philippines. Let’s make square roots a fun part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

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

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