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Last updated on April 10th, 2025

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Square Root of -28

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If a number is multiplied by itself, the result is a square. The inverse of the square is the square root. The concept of the square root extends to complex numbers when dealing with negative numbers. Here, we will discuss the square root of -28.

Square Root of -28 for Thai Students
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What is the Square Root of -28?

The square root is the inverse of the square of a number. Since -28 is negative, its square root is not a real number. Instead, it is expressed in terms of imaginary numbers. The square root of -28 can be expressed as √(-28) = √(28) * √(-1) = 2√7 * i, where i is the imaginary unit such that i² = -1.square root of minus 28

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Finding the Square Root of -28

To find the square roots of negative numbers, we use imaginary numbers. The process involves separating the square root of the positive component and the imaginary unit. Let us explore the methods: Separation into real and imaginary components Prime factorization of the positive part Expressing in terms of i

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Square Root of -28 by Prime Factorization Method

First, we find the prime factorization of the positive component, 28.

 

Step 1: Prime factorization of 28 28 = 2 x 2 x 7 = 2² x 7

 

Step 2: Take the square root of the positive part separately √28 = √(2² x 7) = 2√7

 

Step 3: Combine with the imaginary unit Since the original number is negative, we multiply by the imaginary unit: 2√7 * i.

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Square Root of -28 by Separation into Real and Imaginary Parts

The square root of -28 involves the imaginary unit. Here's how to express it:

 

Step 1: Recognize the negative sign The negative sign indicates an imaginary component.

 

Step 2: Factor the positive and imaginary parts separately √(-28) = √(28) * √(-1)

 

Step 3: Solve for the components √28 = 2√7 √(-1) = i

 

Step 4: Express the result The result is 2√7 * i, representing the square root of -28.

Professor Greenline from BrightChamps

Applications and Implications of Square Roots of Negative Numbers

Understanding square roots of negative numbers is crucial in fields involving complex analysis and electrical engineering. Imaginary numbers are used to model real-world phenomena like AC circuits and oscillations.

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Visualizing the Square Root of -28 on the Complex Plane

The complex plane is a tool used to visualize complex numbers. The square root of -28 can be represented as a point on this plane.

 

Step 1: The real part is 0

 

Step 2: The imaginary part is 2√7 This point (0, 2√7) is located on the imaginary axis, as there is no real component.

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Common Mistakes and How to Avoid Them in the Square Root of -28

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Square Root of -28 Examples

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Problem 1

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

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Explanation

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Max, the Girl Character from BrightChamps

Problem 2

A complex number is given as 3 + √(-16). Express it in standard form.

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Explanation

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Problem 3

Calculate 2 * √(-9).

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Explanation

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Problem 4

What is the square root of (-36) in terms of its real and imaginary parts?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 5

If z = √(-25), what is the modulus of z?

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Explanation

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FAQ on Square Root of -28

1.What is √(-28) in terms of i?

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2.What are the factors of 28?

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3.How is the square root of a negative number defined?

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4.Can negative numbers have real square roots?

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5.What is the square root of -1?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -28

  • Imaginary Unit: The imaginary unit i is defined such that i² = -1. It is used to express the square roots of negative numbers.
     
  • Complex Number: A complex number has a real part and an imaginary part, expressed as a + bi, where a and b are real numbers.
     
  • Prime Factorization: Breaking down a number into its prime components. For example, the prime factorization of 28 is 2² x 7.
     
  • Modulus: The modulus of a complex number is its distance from the origin on the complex plane, calculated as the square root of the sum of squares of its real and imaginary parts.
     
  • Complex Plane: A two-dimensional plane used to represent complex numbers, with the real part on the x-axis and the imaginary part on the y-axis.
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 -28 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!
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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.

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Fun Fact

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

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