BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon101 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of -91

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 -91.

Square Root of -91 for Bahraini Students
Professor Greenline from BrightChamps

What is the Square Root of -91?

The square root is the inverse of the square of the number. Since -91 is a negative number, it does not have a real number square root. In the context of complex numbers, the square root of -91 can be expressed using the imaginary unit 'i'. The square root of -91 is expressed as √(-91) = √91 * i, which is approximately 9.5394i, an imaginary number.

Professor Greenline from BrightChamps

Finding the Square Root of -91

The prime factorization method, long division method, and approximation method are typically used for real numbers. However, since -91 is negative, these methods do not directly apply. Instead, we can express the square root in terms of imaginary numbers.

Professor Greenline from BrightChamps

Square Root of -91 by Imaginary Numbers

To find the square root of a negative number, we incorporate the imaginary unit 'i', where i = √(-1).

 

Step 1: We express the square root of -91 as √(-91) = √91 * √(-1).

 

Step 2: Since √(-1) = i, we have √(-91) = √91 * i.

 

Step 3: Calculate √91, which is approximately 9.5394.

 

Step 4: The square root of -91 is then approximately 9.5394i, an imaginary number.

Professor Greenline from BrightChamps

Common Mistakes when Dealing with Square Roots of Negative Numbers

When working with square roots of negative numbers, it's essential to understand the role of the imaginary unit 'i' and not to apply real number methods directly.

Professor Greenline from BrightChamps

Understanding the Properties of Imaginary Numbers

Imaginary numbers are essential when dealing with square roots of negative numbers. The key property is that i² = -1, and this helps in simplifying expressions involving square roots of negative numbers.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of -91

Students often make mistakes when dealing with square roots of negative numbers, such as ignoring the imaginary unit or incorrectly applying real number methods. Here are some common mistakes and how to avoid them.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting the Imaginary Unit 'i'

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

When calculating the square root of a negative number, it is crucial to include the imaginary unit 'i'.

 

For example, forgetting to write √(-91) as 9.5394i can lead to incorrect conclusions.

Max from BrightChamps Saying "Hey"

Square Root of -91 Examples

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

Problem 1

Can you help Max find the square root of -64 using imaginary numbers?

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

The square root of -64 is ±8i.

Explanation

To find the square root of -64, express it as √(-64) = √64 * √(-1). Since √64 = 8 and √(-1) = i, the square root of -64 is ±8i.

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

Problem 2

A field has an area of -91 square meters. What is the side length if measured using imaginary numbers?

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

The side length is approximately ±9.5394i meters.

Explanation

The side length of a square field with an area -91 square meters can be found by taking the square root of -91, which is approximately ±9.5394i meters.

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

Problem 3

Calculate √(-91) * 3 using imaginary numbers.

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

The result is approximately ±28.6182i.

Explanation

First, find the square root of -91, which is approximately ±9.5394i. Multiply this by 3 to get ±28.6182i.

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

Problem 4

What is the product of √(-25) and √(-4)?

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

The product is ±10i² or ±(-10).

Explanation

First, find the square roots: √(-25) = ±5i and √(-4) = ±2i. Multiply them to get ±10i². Since i² = -1, the result is ±(-10).

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

Problem 5

If the width of a rectangular field is √(-49)i meters, and the length is 14 meters, what is the perimeter?

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

The perimeter is not a real number, but it includes imaginary components.

Explanation

The perimeter formula is 2 * (length + width). Using the imaginary width: 2 * (14 + 7i) = 28 + 14i. The perimeter includes an imaginary component.

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

FAQ on Square Root of -91

1.What is √(-91) in terms of imaginary numbers?

Math FAQ Answers Dropdown Arrow

2.Can the square root of a negative number be a real number?

Math FAQ Answers Dropdown Arrow

3.What is the imaginary unit 'i'?

Math FAQ Answers Dropdown Arrow

4.How do you express the square root of a negative number?

Math FAQ Answers Dropdown Arrow

5.What are complex numbers?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of -91?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of -91?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, we understand algebra as more than symbols—it’s a gateway to countless opportunities! We are dedicated to helping children across Bahrain master essential math skills, focusing today on the Square Root of -91 with special attention to square roots—in a fun, lively, and easy-to-follow manner. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, following local football scores, or managing their allowance to buy the latest gadgets, mastering algebra builds confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Because kids in Bahrain learn differently, we customize our teaching to fit each learner’s style. From Manama’s lively city life to peaceful beaches, BrightChamps brings math to life, making it exciting throughout Bahrain. Let’s make square roots a fun 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