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Last updated on May 26th, 2025

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Square Root of -47

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The square root is the inverse operation of squaring a number. In real numbers, the square root of a negative number is not defined. However, in the field of complex numbers, the square root of a negative number is expressed using imaginary units. Here, we will discuss the square root of -47.

Square Root of -47 for UAE Students
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What is the Square Root of -47?

The square root of a negative number is not defined in the real number system. Instead, it is expressed in terms of imaginary numbers. The square root of -47 is expressed as √(-47) or in terms of imaginary units as i√47, where i is the imaginary unit defined as √(-1). Therefore, the square root of -47 is an imaginary number.

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Finding the Square Root of -47

For negative numbers, the square root is not defined in the real number system. Instead, we use the concept of imaginary numbers. The methods used for finding the square root of positive numbers such as prime factorization, long division, or approximation do not apply directly to negative numbers. Instead, we consider the imaginary unit: - Imaginary unit method

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Square Root of -47 by Imaginary Unit Method

The imaginary unit method is used to express the square root of a negative number. Let's see how:

 

Step 1: Identify the negative number, which is -47.

 

Step 2: Express -47 as (-1) x 47.

 

Step 3: The square root of -1 is represented by the imaginary unit i.

 

Step 4: Therefore, the square root of -47 is expressed as i√47.

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Square Root of -47 by Complex Number Representation

In the complex number system, the square root of any negative number can be expressed by separating the negative part using the imaginary unit:

 

Step 1: Write the number -47 as the product of -1 and 47.

 

Step 2: Recognize that √(-1) is the imaginary unit i.

 

Step 3: Express the square root of -47 as i√47, indicating it is a complex number.

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Applications of Imaginary Numbers in Real Life

Though imaginary numbers are not part of the real number system, they have applications in various fields: - Electrical engineering: Used in the analysis of AC circuits with complex impedance. - Control theory: Utilized in system stability analysis. - Signal processing: Applied to handle waveforms and oscillations. - Quantum physics: Used to describe wave functions and quantum states.

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Common Mistakes and How to Avoid Them in the Square Root of -47

Mistakes are often made when dealing with negative square roots, especially when applying real number methods. Let’s explore a few common errors and how to avoid them.

Mistake 1

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Ignoring the Imaginary Unit

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It’s crucial to remember that the square root of a negative number involves the imaginary unit. Forgetting to include 'i' can lead to incorrect results.

For example, √(-47) is not simply √47, but i√47.

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Square Root of -47 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max express the square root of -64 in terms of imaginary numbers?

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The square root of -64 is 8i.

Explanation

First, express -64 as (-1) x 64.

The square root of -1 is i, and the square root of 64 is 8.

Therefore, the square root of -64 is 8i.

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Problem 2

What is the result of multiplying the square root of -47 by 2i?

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The result is -94.

Explanation

First, express the square root of -47 as i√47.

Multiply i√47 by 2i: (i√47) x (2i) = 2i^2√47 = 2(-1)√47 = -2√47.

Since √47 is irrational, the exact numerical result is expressed as -2√47.

However, the imaginary units combine to give the real negative result -94.

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Max, the Girl Character from BrightChamps

Problem 3

If the square root of a negative number is expressed in terms of i, what is i^2?

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i^2 is equal to -1.

Explanation

The imaginary unit i is defined as the square root of -1.

Therefore, i^2 = (-1).

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Problem 4

What is the simplified form of (3 + i√47) x (3 - i√47)?

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The simplified form is -47 + 9 = -38.

Explanation

Apply the difference of squares formula: (a + b)(a - b) = a^2 - b^2.

Here, a = 3 and b = i√47.

So, (3 + i√47)(3 - i√47) = 3^2 - (i√47)^2 = 9 - (-47) = 9 + 47 = 56.

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Problem 5

Calculate √(-47) x √(-1).

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The result is i^2√47 = -47.

Explanation

Express √(-47) as i√47 and √(-1) as i.

The multiplication gives i√47 x i = i^2√47 = -1 x √47 = -47.

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FAQ on Square Root of -47

1.What is the square root of -47 in terms of real numbers?

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2.What does the symbol i represent?

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

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4.Is -47 a perfect square?

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

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6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of -47?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of -47?

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9.Does learning Algebra support future career opportunities for students in United Arab Emirates?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -47

  • Imaginary unit: The imaginary unit, denoted as i, is defined as the square root of -1. It is used to express the square roots of negative numbers.
     
  • Complex number: A complex number is a number that has both a real and an imaginary part, expressed in the form a + bi, where a and b are real numbers.
     
  • Real number: A real number is a value that represents a quantity along a continuous line, including all rational and irrational numbers, but not imaginary numbers.
     
  • Perfect square: A perfect square is a number that is the square of an integer.
     
  • Non-real number: A non-real number is a number that cannot be represented on the real number line, typically involving imaginary numbers.
Professor Greenline from BrightChamps

About BrightChamps in United Arab Emirates

At BrightChamps, we know algebra is more than symbols—it opens doors to endless possibilities! We’re dedicated to helping kids throughout the UAE develop crucial math skills, focusing today on the Square Root of -47 with a special focus on square roots—in an enjoyable, engaging, and easy-to-understand way. Whether your child is figuring out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of local football scores, or budgeting their allowance for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons make learning both fun and simple. Because kids in the UAE learn in varied ways, we customize our teaching to fit each child’s needs. From Dubai’s soaring skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps brings math alive, making it relevant and exciting throughout the UAE. 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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Max, the Girl Character from BrightChamps

Fun Fact

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

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