Last updated on May 26th, 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.
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.
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 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.
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.
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.
Students often make mistakes while finding square roots, such as neglecting the negative square root or misapplying methods. Let's explore these common mistakes:
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.
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.
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
Divide the total area by 2: 5/6 ÷ 2
= 5/12
≈ 0.41665 square meters.
Calculate √(5/6) × 4.
Approximately 3.6515
First, find the square root of 5/6, which is approximately 0.91287.
Then multiply by 4: 0.91287 × 4 ≈ 3.6515
What will be the square root of (5/6 + 1/6)?
The square root is 1.
First, find the sum: (5/6 + 1/6) = 6/6 = 1.
The square root of 1 is ±1.
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.
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√(5/6) + 1)
= 2 × (0.91287 + 1)
= 3.82574 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.