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Last updated on April 9th, 2025

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Square Root of -128

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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 various fields, including vehicle design, finance, etc. Here, we will discuss the square root of -128.

Square Root of -128 for Thai Students
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What is the Square Root of -128?

The square root is the inverse of the square of the number. Since -128 is a negative number, it does not have a real square root. Instead, the square root of -128 is expressed in terms of imaginary numbers. In radical form, it is expressed as √-128 = √128 * i, where i is the imaginary unit. In exponential form, it can be written as (128)^(1/2) * i. Simplifying further, √128 = 8√2, so √-128 = 8√2 * i, which is an imaginary number.square root of minus 128

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Finding the Square Root of -128

Since -128 is a negative number, we use the concept of imaginary numbers to find its square root. The prime factorization method, long division method, and approximation method are not applicable for negative numbers in the context of real numbers. Instead, we find the square root of the absolute value and multiply it by i:

 

Step 1: Find the square root of the absolute value, 128.

 

Step 2: Include the imaginary unit i to represent the square root of -128.

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Square Root of 128 by Prime Factorization Method

To find the square root of 128, we use the prime factorization method.

 

Step 1: Find the prime factors of 128. Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^7.

 

Step 2: Pair the prime factors. Since 128 is not a perfect square, we can pair the 2s: 2^7 = (2^3 * 2^3) * 2 = (8 * 8) * 2.

 

Step 3: The square root of 128 is 8√2. Therefore, the square root of -128 is 8√2 * i.

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Square Root of -128 by Imaginary Unit

To find the square root of a negative number like -128, we use the imaginary unit i, where i^2 = -1.

 

Step 1: Find the square root of the positive number 128, which is 8√2.

 

Step 2: Multiply the result by i to account for the negative sign. So the square root of -128 is 8√2 * i.

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Understanding Negative Square Roots

The concept of negative square roots involves imaginary numbers, as real numbers do not have square roots for negative values.

 

Step 1: Recognize that for any negative number, the square root involves i.

 

Step 2: Calculate the square root of the positive equivalent, and multiply by i. For example, √-128 = √128 * i = 8√2 * i.

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Common Mistakes and How to Avoid Them in the Square Root of -128

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Square Root of -128 Examples

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Problem 1

Can you help Max find the square root of -128 in terms of imaginary numbers?

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Explanation

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Problem 2

If a complex number is given as √-128, what is its real and imaginary part?

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Explanation

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Problem 3

Calculate 2 times the square root of -128.

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Explanation

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Problem 4

What is the square of the imaginary unit i?

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Explanation

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Problem 5

How do you express √-128 in terms of a complex number?

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Explanation

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FAQ on Square Root of -128

1.What is √-128 in terms of imaginary numbers?

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2.Why can't we find a real square root of -128?

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3.How do you find the square root of a negative number?

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4.What is the principal square root of a negative number?

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5.Is √-128 a real number?

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

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7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of -128?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of -128?

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

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Important Glossaries for the Square Root of -128

  • Square root: The square root is the inverse operation of squaring a number. For negative numbers, it involves imaginary numbers.
     
  • Imaginary number: An imaginary number is a number that can be expressed in the form of a real number multiplied by the imaginary unit i.
     
  • Imaginary unit: The imaginary unit i is defined such that i^2 = -1, used to express square roots of negative numbers.
     
  • Complex number: A complex number consists of a real part and an imaginary part, expressed as a + bi.
     
  • Absolute value: The absolute value of a number is its non-negative value, used when finding square roots of negative numbers.
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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 -128 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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