BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon125 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 86

Professor Greenline Explaining Math Concepts

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 86.

Square Root of 86 for Thai Students
Professor Greenline from BrightChamps

What is the Square Root of 86?

The square root is the inverse of the square of the number. 86 is not a perfect square. The square root of 86 is expressed in both radical and exponential form.

In radical form, it is expressed as √86, whereas (86)(1/2) in the exponential form. √86 ≈ 9.2736, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Professor Greenline from BrightChamps

Finding the Square Root of 86

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:

 

  1. Prime factorization method
  2. Long division method
  3. Approximation method
Professor Greenline from BrightChamps

Square Root of 86 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 86 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 86 Breaking it down, we get 2 x 43: 21 x 431

 

Step 2: Now we have found the prime factors of 86. The second step is to make pairs of those prime factors. Since 86 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating 86 using prime factorization is impossible.

Professor Greenline from BrightChamps

Square Root of 86 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 86, we need to group it as 86.

 

Step 2: Now we need to find n whose square is ≤ 86. We can say n as ‘9’ because 9 x 9 = 81, which is less than 86. The quotient is 9, and after subtracting 81 from 86, the remainder is 5.

 

Step 3: Since there are no more digits to bring down, we need to add a decimal point and bring down two zeros to make the dividend 500.

 

Step 4: Double the previous quotient (9) to get 18, which will be our new divisor prefix. We need to find a digit x such that 18x x x ≤ 500.

 

Step 5: Let x be 2, then 182 x 2 = 364.

 

Step 6: Subtract 364 from 500 to get 136, and the quotient is now 9.2.

 

Step 7: Since the remainder is not zero, we repeat the process by bringing down more pairs of zeros and finding the next digit. Continue until you reach the desired precision.

 

So, the square root of √86 is approximately 9.2736.

Professor Greenline from BrightChamps

Square Root of 86 by Approximation Method

The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 86 using the approximation method.

 

Step 1: Find the closest perfect squares to 86. The smallest perfect square less than 86 is 81, and the largest perfect square greater than 86 is 100. √86 falls somewhere between 9 and 10.

 

Step 2: Apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (86 - 81) / (100 - 81) = 5 / 19 ≈ 0.263.

 

Step 3: Add the decimal to the smaller root: 9 + 0.263 = 9.263.

 

So, the square root of 86 is approximately 9.2736.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 86

Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting about the negative square root

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.

For example: √86 ≈ 9.2736, there is also -9.2736 which should not be forgotten.

Max from BrightChamps Saying "Hey"

Square Root of 86 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 √86?

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

The area of the square is 86 square units.

Explanation

The area of the square = side2.

 

The side length is given as √86. Area of the square = side2 = √86 x √86 = 86.

 

Therefore, the area of the square box is 86 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 86 square feet is built; if each of the sides is √86, what will be the square feet of half of the building?

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

43 square feet.

Explanation

We can just divide the given area by 2 as the building is square-shaped.

 

Dividing 86 by 2, we get 43. So half of the building measures 43 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √86 x 5.

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

46.368

Explanation

The first step is to find the square root of 86, which is approximately 9.2736.

 

The second step is to multiply 9.2736 by 5. So 9.2736 x 5 ≈ 46.368.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (81 + 5)?

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

The square root is approximately 9.2736.

Explanation

To find the square root, we need to find the sum of (81 + 5). 81 + 5 = 86, and then √86 ≈ 9.2736.

 

Therefore, the square root of (81 + 5) is approximately ±9.2736.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √86 units and the width ‘w’ is 38 units.

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

We find the perimeter of the rectangle as 94.5472 units.

Explanation

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

 

Perimeter = 2 × (√86 + 38) ≈ 2 × (9.2736 + 38)

 

= 2 × 47.2736

 

= 94.5472 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 86

1.What is √86 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 86.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 86.

Math FAQ Answers Dropdown Arrow

4.Is 86 a prime number?

Math FAQ Answers Dropdown Arrow

5.86 is divisible by?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 86?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 86?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 86

  • Square root: A square root is the inverse operation of squaring a number. For example, 32 = 9, so the square root of 9 is 3: √9 = 3.

 

  • Irrational number: An irrational number is a number that cannot be written as a simple fraction, meaning it cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.

 

  • Principal square root: The principal square root is the non-negative square root of a number. For example, the principal square root of 25 is 5.

 

  • Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 86 is 2 x 43.

 

  • Decimal: A decimal number is a number that consists of a whole number and a fractional part separated by a decimal point. For example, 9.2736 is a decimal number. ```
Professor Greenline from BrightChamps

About BrightChamps in Thailand

At BrightChamps, we understand algebra is more than just symbols—it opens up a world of opportunities! Our mission is to help children across Thailand develop essential math skills, focusing today on the Square Root of 86 with a special look at square roots—in a lively, enjoyable, and easy-to-follow manner. Whether your child is discovering the speed of a roller coaster at Dream World, tallying local football scores, or managing their allowance to buy the latest gadgets, mastering algebra gives them confidence for everyday life. Our interactive lessons make learning fun and straightforward. Since children in Thailand have varied learning styles, we personalize our approach for each child. From Bangkok’s busy streets to Phuket’s tropical islands, BrightChamps brings math to life, making it relatable and exciting throughout Thailand. Let’s make square roots a joyful part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

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

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom