BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon100 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of -56

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 -56.

Square Root of -56 for Filipino Students
Professor Greenline from BrightChamps

What is the Square Root of -56?

The square root is the inverse of the square of the number. Since -56 is a negative number, its square root involves imaginary numbers. The square root of -56 is expressed in both radical and exponential form. In the radical form, it is expressed as √(-56), whereas (-56)^(1/2) in exponential form. The principal square root of -56 is expressed as √(-56) = 7.48331i, where i is the imaginary unit, because the square root of a negative number is not a real number.

Professor Greenline from BrightChamps

Finding the Square Root of -56

For negative numbers, the square root involves imaginary numbers. The methods used for finding square roots of positive numbers are not directly applicable. However, we can express the square root of a negative number using the imaginary unit i. The steps are as follows:

 

1. Separate the negative sign from the number.

2. Find the square root of the positive part.

3. Multiply the result by i, the imaginary unit.

Professor Greenline from BrightChamps

Square Root of -56 by Prime Factorization Method

Prime factorization is typically used for non-negative numbers. However, we can adopt the process to find the square root of the positive part:

 

Step 1: Finding the prime factors of 56 Breaking it down, we get 2 x 2 x 2 x 7: 2^3 x 7^1

 

Step 2: Now, we found the prime factors of 56. Since -56 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.

 

The square root of -56 is expressed as √(-56) = √(56) x i = √(2^3 x 7) x i = 2√(14) x i.

Professor Greenline from BrightChamps

Square Root of -56 by Long Division Method

The long division method is typically used for positive numbers, so we adapt it for the positive part of -56:

 

Step 1: Consider the positive part, 56, and group the numbers from right to left.

 

Step 2: Find n whose square is closest to 56. For 56, n is approximately 7, since 7^2 = 49.

 

Step 3: Calculate further for better approximation if necessary. However, since we aim for the imaginary square root, the interest is more in identifying the pattern of the imaginary unit: √(-56) = √(56) x i = 7.48331i.

Professor Greenline from BrightChamps

Square Root of -56 by Approximation Method

The approximation method provides a quick way to find the square root of the positive part before applying the imaginary unit:

 

Step 1: Identify √56, which lies between √49 (7) and √64 (8).

 

Step 2: Use the approximation formula (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). For √56: (56 - 49) / (64 - 49) = 7/15 = 0.4667 Add this to 7: 7 + 0.4667 = 7.4667

 

So, √(-56) = 7.4667i

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Finding the Square Root of -56

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

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting the Imaginary Unit

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is crucial to remember that the square root of a negative number involves the imaginary unit i. The square root of -56 should be represented as √(-56) = √(56) x i.

Max from BrightChamps Saying "Hey"

Square Root of -56 Examples

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

Problem 1

If a square has an area of -56 square units, what is the side length?

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

The side length is 7.48331i units.

Explanation

The area of a square is side^2.

For an area of -56, side = √(-56) = 7.48331i.

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

Problem 2

What is the product of √(-56) and 3?

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

22.44993i

Explanation

Calculate √(-56) = 7.48331i.

Then, multiply by 3: 7.48331i x 3 = 22.44993i.

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

Problem 3

Calculate (√(-56))^2.

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

-56

Explanation

By definition, (√(-56))^2 = -56, as squaring the square root returns the original value.

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

Problem 4

What is the real part of √(-56)?

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

0

Explanation

The square root of a negative number is purely imaginary, so the real part is 0.

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

Problem 5

Is √(-56) a real number?

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

No

Explanation

The square root of a negative number is not a real number; it is an imaginary number.

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

FAQ on Square Root of -56

1.What is √(-56) in its simplest form?

Math FAQ Answers Dropdown Arrow

2.What is the principal square root of -56?

Math FAQ Answers Dropdown Arrow

3.Is the square root of -56 a real number?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

5.Why do negative numbers have imaginary square roots?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of -56?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Philippines support learning Algebra and Square Root of -56?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -56

  • 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 the imaginary unit.
     
  • Imaginary number: A number that can be expressed in terms of i, where i is the square root of -1.
     
  • Imaginary unit (i): The symbol used to represent the square root of -1, crucial for square roots of negative numbers.
     
  • Complex number: A number composed of a real and an imaginary part.
     
  • Prime factorization: Expressing a number as a product of its prime factors, useful in simplifying square roots of positive numbers.
Professor Greenline from BrightChamps

About BrightChamps in Philippines

At BrightChamps, we believe algebra is more than symbols—it’s a gateway to countless opportunities! Our mission is to support children across the Philippines in mastering key math skills, focusing today on the Square Root of -56 with an emphasis on understanding square roots—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy the latest gadgets, mastering algebra builds their confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different styles, we tailor our approach to each learner. From Manila’s busy streets to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting and relevant throughout the Philippines. 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