125 LearnersLast updated on May 26th, 2025
Square Root of 5/6
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.
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:
Mistake 1
Forgetting about the negative square root
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.
Mistake 2
Not converting fractions to decimals properly
When dealing with fractions, it's crucial to convert them accurately to decimals for calculation.
For example, miscalculating 5/6 as 0.85 instead of 0.8333 can lead to errors.
Mistake 3
Misplacing the square root symbol
Placing the square root symbol incorrectly leads to wrong results.
For example, √5/6 is not the same as √(5/6).
Mistake 4
Confusing square root with cube root
Square roots and cube roots are often confused.
For example, √(5/6) and ∛(5/6) are different, and confusing them can lead to incorrect outcomes.
Mistake 5
Errors in long division
The long division method involves many steps. Skipping a step or making an arithmetic mistake can lead to incorrect results. Careful attention to detail is necessary.
Square Root of 5/6 Examples
Problem 1
Can you help Alex find the area of a square box if its side length is given as √(5/6)?
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.
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?
0.41665 square meters
Explanation
Divide the total area by 2: 5/6 ÷ 2
= 5/12
≈ 0.41665 square meters.
Problem 3
Calculate √(5/6) × 4.
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
Problem 4
What will be the square root of (5/6 + 1/6)?
The square root is 1.
Explanation
First, find the sum: (5/6 + 1/6) = 6/6 = 1.
The square root of 1 is ±1.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(5/6) units and the width ‘w’ is 1 unit.
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.
FAQ on Square Root of 5/6
1.What is √(5/6) in its simplest form?
2.What are the factors of 5/6?
3.Calculate the square of 5/6.
4.Is 5/6 a prime number?
5.Is 5/6 divisible by any other numbers?
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.
