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 -73

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 -73.

Square Root of -73 for US Students
Professor Greenline from BrightChamps

What is the Square Root of -73?

The square root is the inverse of the square of the number. The number -73 does not have a real square root because it is negative. However, it does have an imaginary square root. The square root of -73 can be expressed in both radical and exponential form with an imaginary unit. In radical form, it is expressed as √(-73), whereas (-73)^(1/2) in exponential form. The square root of -73 is an imaginary number because it involves the square root of a negative number, which is not defined in the set of real numbers.

Professor Greenline from BrightChamps

Finding the Square Root of -73

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are typically used. However, for negative numbers, we use the concept of imaginary numbers. Let us explore the following methods:

 

  • Imaginary number concept
Professor Greenline from BrightChamps

Square Root of -73 Using Imaginary Number Concept

For a negative number, the square root involves the imaginary unit 'i', which is defined as √(-1). Now, let's express the square root of -73:

 

Step 1: Recognize that -73 is negative.

 

Step 2: Express √(-73) as √(73) * √(-1).

 

Step 3: Simplify to get √73 * i.

 

Since 73 is not a perfect square, √73 remains as it is in its simplest radical form.

Professor Greenline from BrightChamps

Square Root of -73 by Approximation Method

The approximation method can be used to find the square root of positive numbers, but here we apply it in terms of absolute value:

 

Step 1: Find the closest perfect squares to 73. The closest perfect square below 73 is 64, and the closest perfect square above 73 is 81. Hence, √73 falls between 8 and 9.

 

Step 2: Approximate √73 to be closer to 8.5 based on its position between 64 and 81.

 

Step 3: Since we are dealing with -73, the final expression is approximately 8.5i.

Professor Greenline from BrightChamps

Imaginary Numbers and Their Importance

Imaginary numbers extend the concept of square roots to negative numbers. They are crucial in various fields such as electrical engineering, quantum physics, and applied mathematics. Understanding how to handle these numbers is essential for complex problem-solving.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of -73

Students often make mistakes while finding the square root, such as misunderstanding imaginary numbers or incorrectly simplifying radicals. Let's look at some of these common mistakes in detail.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Misunderstanding Imaginary Numbers

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It's crucial to understand that the square root of a negative number involves the imaginary unit 'i'.

For example, √(-73) is not a real number but rather an imaginary number, expressed as √73 * i.

Max from BrightChamps Saying "Hey"

Square Root of -73 Examples

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

Problem 1

Can you help Max find the expression of the square root of -50?

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

The expression is 5√2 * i.

Explanation

The square root of -50 is expressed as √(-50) = √(50) * √(-1) = √(25 * 2) * i = 5√2 * i.

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

Problem 2

If a complex number z is defined as z = √(-73) + 5, what is the imaginary part of z?

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

The imaginary part is approximately 8.5.

Explanation

The complex number z = √(-73) + 5 is broken down into real and imaginary parts.

The imaginary part is √73 * i, which is approximately 8.5i.

Hence, the imaginary part is approximately 8.5.

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

Problem 3

Calculate 2 * √(-73).

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

Approximately 17i.

Explanation

First, determine √(-73) = √73 * i.

Approximating √73 as 8.5, we have 2 * 8.5 * i = 17i.

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

Problem 4

What will be the square root of (-36)?

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

The square root is 6i.

Explanation

To find the square root, express √(-36) as √(36) * √(-1) = 6 * i.

Therefore, the square root of (-36) is ±6i.

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

Problem 5

If a rectangle has a length of √(-49) and a width of 5, what is the area in terms of i?

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

The area is 35i square units.

Explanation

Area of the rectangle = length * width.

The length is √(-49) = 7i.

Thus, the area = 7i * 5 = 35i square units.

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

FAQ on Square Root of -73

1.What is √(-73) in its simplest form?

Math FAQ Answers Dropdown Arrow

2.What is the imaginary unit?

Math FAQ Answers Dropdown Arrow

3.Why can't negative numbers have real square roots?

Math FAQ Answers Dropdown Arrow

4.Can we approximate √(-73)?

Math FAQ Answers Dropdown Arrow

5.How are imaginary numbers used in engineering?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of -73?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in United States support learning Algebra and Square Root of -73?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -73

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, it involves imaginary numbers.
     
  • Imaginary number: A number that can be written as a real number multiplied by the imaginary unit 'i', where i is the square root of -1.
     
  • Complex number: A number that has both a real part and an imaginary part, expressed in the form a + bi.
     
  • Radical: An expression that includes a root symbol (√) and represents the root of a number.
     
  • Approximation: The process of estimating a number by finding a close but not exact value, often used for non-perfect squares.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of -73, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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