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Last updated on May 26th, 2025

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Square Root of -143

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The square of a number is obtained by multiplying the number by itself. The inverse operation of squaring a number is finding its square root. Square roots are applicable in various fields, such as engineering, physics, and finance. In this discussion, we will explore the concept of the square root of -143.

Square Root of -143 for Omani Students
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What is the Square Root of -143?

The square root of a number is a value that, when multiplied by itself, gives the original number. However, -143 is a negative number, and the square root of a negative number is not a real number. In mathematics, the square root of a negative number is expressed using the imaginary unit, denoted as 'i', where i = √-1. Therefore, the square root of -143 is expressed as √-143 = √143 * √-1 = √143 * i. The value √143 is approximately 11.958, and thus √-143 is approximately 11.958i, an imaginary number.

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Understanding the Square Root of Negative Numbers

To understand the square root of a negative number, we use the concept of imaginary numbers. The square root of any negative number can be expressed in terms of 'i'. For example, √-143 can be rewritten as √143 * i. Imaginary numbers extend the real number system and are used in advanced fields like electrical engineering and quantum physics.

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Square Root of -143 in Radical and Exponential Form

The square root of -143 can be expressed in both radical and exponential forms: - Radical form: √-143 = √143 * i - Exponential form: (-143)^(1/2) = (143^(1/2)) * i Since -143 is not a perfect square, its square root involves an irrational component (√143) and an imaginary component (i).

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Calculating the Square Root of -143

Since -143 is negative, its square root is not a real number, and we use imaginary numbers to express it. Here's how you calculate it: 1. Find the square root of the positive component: √143 ≈ 11.958 2. Combine with the imaginary unit: √-143 = 11.958i

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Applications of Imaginary Numbers

Imaginary numbers, including the square roots of negative numbers, have practical applications in various fields:

 

1. Electrical Engineering: Used in analyzing AC circuits.

 

2. Control Systems: Imaginary numbers help in the stability analysis of systems.

 

3. Quantum Mechanics: Used to describe wave functions.

 

4. Signal Processing: Complex numbers simplify the mathematical analysis of signals.

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Common Mistakes and How to Avoid Them when Dealing with Square Roots of Negative Numbers

Students often make mistakes when dealing with the square roots of negative numbers, such as ignoring the imaginary unit or misapplying square root properties. Here are some common mistakes and how to avoid them.

Mistake 1

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Ignoring the Imaginary Unit

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A common mistake is to overlook the imaginary unit 'i' when calculating the square root of a negative number. Remember that the square root of a negative number must include 'i'.

For example, the square root of -25 is not 5, but 5i.

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Examples Involving the Square Root of -143

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Problem 1

What is the result of multiplying the square root of -143 by 2?

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The result is 23.916i.

Explanation

First, find the square root of -143, which is approximately 11.958i.

Then multiply by 2: 11.958i * 2 = 23.916i.

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Problem 2

If x = √-143, what is x^2?

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x^2 = -143.

Explanation

By definition, if x = √-143, then x^2 = (√-143)^2 = -143.

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Problem 3

Express the square root of -143 in terms of real and imaginary components.

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The square root of -143 can be expressed as 0 + 11.958i.

Explanation

The expression √-143 = √143 * i, where √143 ≈ 11.958.

Therefore, the real part is 0 and the imaginary part is 11.958i.

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FAQ on the Square Root of -143

1.What is the square root of -143 in its simplest form?

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2.Can the square root of a negative number be a real number?

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3.Is the square root of -143 a rational number?

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4.What is the imaginary unit 'i'?

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

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

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of -143?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of -143?

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

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Important Glossaries for the Square Root of -143

  • Imaginary Number: A number that can be written as a real number multiplied by the imaginary unit 'i', which is defined as √-1.

 

  • Complex Number: A number comprising both a real and an imaginary part, generally expressed as a + bi, where a and b are real numbers.

 

  • Radical: A symbol (√) representing the root of a number. For negative numbers, it involves the imaginary unit 'i'.

 

  • Irrational Number: A number that cannot be expressed as a simple fraction, often involving non-terminating, non-repeating decimals.

 

  • Exponential Form: A way to express numbers using powers, often used with complex numbers to represent roots, such as (-143)^(1/2).
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About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of -143 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. 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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