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Last updated on May 26th, 2025

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Square Root of -200

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If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The concept of square roots is used in various fields such as engineering, finance, and physics. Here, we will discuss the square root of -200.

Square Root of -200 for Thai Students
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What is the Square Root of -200?

The square root is the inverse of the square of the number. The number -200 is negative, and the square root of a negative number is not a real number. The square root of -200 is expressed in terms of imaginary numbers. In the radical form, it is expressed as √(-200), whereas in exponential form, it is written as (-200)^(1/2). The square root of -200 is an imaginary number and can be expressed as 10√2i, where "i" is the imaginary unit.

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Finding the Square Root of -200

The prime factorization method is used for perfect square numbers. However, for negative numbers like -200, we use the concept of imaginary numbers. Let's explore the methods:

 

  •  Imaginary unit concept
  •  Approximation method for positive equivalent
  •  Simplification using √(-1)
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Square Root of -200 using Imaginary Unit Concept

The imaginary unit "i" is defined as √(-1). Using this concept, we can express the square root of negative numbers. For -200, we simplify as follows:

 

Step 1: Express -200 as a product of 200 and -1: -200 = 200 × (-1)

 

Step 2: Take the square root of each factor: √(-200) = √(200) × √(-1)

 

Step 3: Simplify using the imaginary unit: √(200) = √(2 × 100) = 10√2, so √(-200) = 10√2i.

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Square Root of 200 by Approximation Method

The approximation method helps find the square root of the positive equivalent of the number. Let's consider 200:

 

Step 1: Identify the nearest perfect squares around 200. The closest perfect squares are 196 (14^2) and 225 (15^2).

 

Step 2: 200 lies between 196 and 225. So, 14 < √200 < 15.

 

Step 3: Approximate using the average method: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square).

 

Using the approximation: (200 - 196) / (225 - 196) ≈ 0.14 Therefore, √200 ≈ 14.14. So, the square root of -200 is approximately 14.14i.

Professor Greenline from BrightChamps

Understanding Imaginary Numbers

Imaginary numbers are used when dealing with the square roots of negative numbers. Here’s how:

 

1. Imaginary unit "i" represents √(-1).

 

2. Any negative square root can be expressed as a product of a real square root and "i".

 

3. For example, the square root of -200 is expressed as 10√2i.

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Common Mistakes and How to Avoid Them in the Square Root of -200

When dealing with negative square roots, students often make errors such as ignoring the imaginary unit or incorrectly simplifying the negative square root. Let's look at some common mistakes in detail.

Mistake 1

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Ignoring the Imaginary Unit

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Some students attempt to find a real number for the square root of a negative number, which is incorrect. Always include "i" to represent the imaginary unit.

For example, instead of √(-200) = 14.14, it should be √(-200) = 14.14i.

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Square Root of -200 Examples

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Problem 1

Can you help Max find the square root of -72?

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The square root of -72 is 6√2i.

Explanation

First, express -72 as a product of 72 and -1: -72 = 72 × (-1).

Then, √(-72) = √(72) × √(-1) = √(36 × 2) × i = 6√2i.

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Problem 2

A complex number is given as 5 + √(-64). Simplify it.

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5 + 8i

Explanation

First, find the square root of -64: √(-64) = √(64) × √(-1) = 8i.

So, the complex number simplifies to 5 + 8i.

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Problem 3

Calculate the product of √(-50) and 2.

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The product is 10i√2.

Explanation

First, find the square root of -50: √(-50) = √(50) × √(-1) = 5√2i.

Then, multiply by 2: 5√2i × 2 = 10i√2.

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Problem 4

What is the result of (√(-81))^2?

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The result is -81.

Explanation

First, find the square root of -81: √(-81) = 9i.

Then, square it: (9i)^2 = 81 × (-1) = -81.

Thus, (√(-81))^2 = -81.

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Problem 5

Find the modulus of the complex number 7 + √(-49).

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The modulus is 10.

Explanation

First, simplify √(-49) as 7i.

The complex number is 7 + 7i.

The modulus is √(7^2 + 7^2) = √(49 + 49) = √98 = 10.

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FAQ on Square Root of -200

1.What is √(-200) in its simplest form?

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

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3.How do you express √(-36) in terms of "i"?

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4.Is the square root of a negative number real or imaginary?

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5.Why can't we have a real square root of a negative 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 -200?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of -200?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -200

  • Imaginary Number: A number that can be written as a real number multiplied by the imaginary unit "i", where i = √(-1).

 

  • Complex Number: A number in the form a + bi, where "a" and "b" are real numbers, and "i" is the imaginary unit.

 

  • Principal Square Root: The non-negative root of a non-negative number or the positive imaginary root of a negative number.

 

  • Modulus: The magnitude of a complex number, calculated as √(a^2 + b^2) for a complex number a + bi.

 

  • Square Root: The value that, when multiplied by itself, gives the original number. For negative numbers, this involves the imaginary unit "i".
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 -200 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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