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Last updated on May 26th, 2025

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Square Root of 5/6

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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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 5/6.

Square Root of 5/6 for Vietnamese Students
Professor Greenline from BrightChamps

What is the Square Root of 5/6?

The square root of a number is the inverse operation of squaring that number. The fraction 5/6 is not a perfect square, so its square root is an irrational number. The square root of 5/6 can be expressed in both radical and exponential forms. In the radical form, it is expressed as √(5/6), whereas in exponential form it is expressed as (5/6)^(1/2). The approximate decimal value of √(5/6) is 0.91287, which is irrational because it cannot be expressed as a fraction of two integers with a non-zero denominator.

Professor Greenline from BrightChamps

Finding the Square Root of 5/6

For rational numbers like fractions, we often use approximation methods to find square roots, especially when the fraction is not a perfect square. We can also use the prime factorization method for each part of the fraction separately. Let us now explore these methods: 

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 5/6 by Prime Factorization Method

Prime factorization involves breaking down numbers into their prime factors. Since 5 and 6 are relatively small numbers, this method can be applied to each part:

 

Step 1: Prime factorize 5 and 6 separately: - 5 is already a prime number. - 6 can be factored as 2 × 3.

 

Step 2: The square root of a fraction is the square root of the numerator divided by the square root of the denominator: √(5/6) = √5 / √6 = √5 / (√2 × √3).

 

Since there are no perfect squares in the factorization, the square root cannot be simplified further using this method.

Professor Greenline from BrightChamps

Square Root of 5/6 by Long Division Method

The long division method can be used to find the square root of non-perfect squares, including fractions. Here's how it works for 5/6:

 

Step 1: Convert 5/6 into a decimal, approximately 0.8333.

 

Step 2: Use the long division method to find the square root of 0.8333. Begin by grouping the decimal digits in pairs from the decimal point.

 

Step 3: Find the largest whole number whose square is less than or equal to 0.83. It is 0.9.

 

Step 4: Subtract 0.81 (0.9 squared) from 0.83, bringing down two zeros to continue the division.

 

Step 5: Repeat the process to find the decimal value with more precision.

 

The approximate value of √(5/6) is 0.91287.

Professor Greenline from BrightChamps

Square Root of 5/6 by Approximation Method

The approximation method is a simpler way to find the square root of a fraction:

 

Step 1: Estimate by finding two perfect squares between which 5/6 lies. For example, 0.8333 lies between 0.81 (0.9^2) and 1 (1^2).

 

Step 2: Use interpolation to estimate the square root: (0.8333 - 0.81) / (1 - 0.81) = (0.0233) / (0.19) = 0.12263.

 

Step 3: Add this to the smaller square root: 0.9 + 0.12263 ≈ 1.02263.

 

The approximate value of √(5/6) is 0.91287.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 5/6

Students often make mistakes while finding square roots, such as neglecting the negative square root or misapplying methods. Let's explore these common mistakes:

Mistake 1

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Forgetting about the negative square root

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A number has both positive and negative square roots. In most practical applications, we use the positive square root.

For instance, if √(5/6) ≈ 0.91287, there is also -0.91287, which is often overlooked.

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Square Root of 5/6 Examples

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

Problem 1

Can you help Alex find the area of a square box if its side length is given as √(5/6)?

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The area of the square is approximately 0.8333 square units.

Explanation

The area of a square = side^2.

If the side length is √(5/6), then: Area = (√(5/6))^2

= 5/6

= 0.8333 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped plot measuring 5/6 square meters is made; if each of the sides is √(5/6), what will be the square meters of half of the plot?

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0.41665 square meters

Explanation

Divide the total area by 2: 5/6 ÷ 2

= 5/12

≈ 0.41665 square meters.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(5/6) × 4.

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Approximately 3.6515

Explanation

First, find the square root of 5/6, which is approximately 0.91287.

Then multiply by 4: 0.91287 × 4 ≈ 3.6515

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (5/6 + 1/6)?

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The square root is 1.

Explanation

First, find the sum: (5/6 + 1/6) = 6/6 = 1.

The square root of 1 is ±1.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(5/6) units and the width ‘w’ is 1 unit.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is approximately 3.82574 units.

Explanation

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

Perimeter = 2 × (√(5/6) + 1)

= 2 × (0.91287 + 1)

= 3.82574 units.

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Ray Thinking Deeply About Math Problems

FAQ on Square Root of 5/6

1.What is √(5/6) in its simplest form?

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2.What are the factors of 5/6?

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3.Calculate the square of 5/6.

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4.Is 5/6 a prime number?

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5.Is 5/6 divisible by any other numbers?

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

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7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 5/6?

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8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 5/6?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 5/6

  • Square Root: A square root is the inverse operation of squaring a number. For example, √4 = 2 because 2^2 = 4.
     
  • Irrational Number: An irrational number cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating.
     
  • Fraction: A fraction represents a part of a whole and is expressed as a numerator divided by a denominator, such as 5/6.
     
  • Decimal: A decimal is a way of expressing fractions in a base-10 system, such as 0.8333 for 5/6.
     
  • Prime Factorization: This is the process of breaking down a number into its basic prime number factors.
Professor Greenline from BrightChamps

About BrightChamps in Vietnam

At BrightChamps, we know algebra is more than symbols—it’s a path to countless opportunities! Our goal is to help children across Vietnam grasp essential math skills, with today’s focus on the Square Root of 5/6 and a special look at square roots—in an engaging, enjoyable, and easy-to-learn way. Whether your child is figuring out how fast a roller coaster moves at Suoi Tien Theme Park, keeping track of local football scores, or budgeting their allowance for new gadgets, mastering algebra gives them the confidence to handle daily challenges. Our interactive lessons make learning easy and fun. Since children in Vietnam learn in different ways, we adapt to each learner’s style. From Ho Chi Minh City’s vibrant streets to the beautiful Ha Long Bay, BrightChamps makes math come alive throughout Vietnam. Let’s make square roots an exciting part of every child’s math adventure!
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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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