Square Root of 5/6
2026-02-28 06:00 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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 5/6.

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.

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

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.

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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.

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.

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:

Problem 1

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

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

0.41665 square meters

Explanation

Divide the total area by 2: 5/6 ÷ 2

= 5/12

≈ 0.41665 square meters.

Well explained 👍

Problem 3

Calculate √(5/6) × 4.

Okay, lets begin

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

Well explained 👍

Problem 4

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

Okay, lets begin

The square root is 1.

Explanation

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

The square root of 1 is ±1.

Well explained 👍

Problem 5

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

Okay, lets 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.

Well explained 👍

FAQ on Square Root of 5/6

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

The square root of 5/6 in simplest form is expressed as √5 / √6, which cannot be simplified further without numerical approximation.

2.What are the factors of 5/6?

The factors of 5/6 are found by considering the factors of the numerator and the denominator separately:

  • Factors of 5: 1, 5
  • Factors of 6: 1, 2, 3, 6

3.Calculate the square of 5/6.

The square of 5/6 is found by squaring both the numerator and the denominator: (5/6)^2 = 25/36 ≈ 0.6944

4.Is 5/6 a prime number?

A fraction like 5/6 is not considered a prime number; prime numbers are whole numbers greater than 1 with only two factors: 1 and themselves.

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

As a fraction, 5/6 is already in its simplest form and cannot be divided further without resulting in a non-integer.

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.

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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.