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Last updated on May 26th, 2025

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Square Root of -55

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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 square root is used in various fields such as engineering and physics. Here, we will discuss the square root of -55.

Square Root of -55 for Saudi Students
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What is the Square Root of -55?

The square root is the inverse of squaring a number. When dealing with negative numbers, the square root involves imaginary numbers, as no real number squared results in a negative. The square root of -55 is expressed using the imaginary unit 'i'. In standard form, it is written as √(-55) = √55 * i, which is an imaginary number.

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Finding the Square Root of -55

Since -55 is a negative number, its square root involves imaginary numbers. We cannot use the typical real-number methods like the prime factorization or long division to find the square root. Instead, we use the concept of imaginary numbers. Let us examine the following approach:

 

  • Imaginary number representation
Professor Greenline from BrightChamps

Square Root of -55 by Imaginary Number Representation

The square root of a negative number is expressed using the imaginary unit 'i', where i² = -1. Therefore, to find √(-55), we express it as √(55) * i. Calculating √55 involves finding the square root of the positive part:

 

Step 1: Approximate the square root of 55. √55 ≈ 7.416

 

Step 2: Combine with the imaginary unit. √(-55) = 7.416i

 

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Common Mistakes and How to Avoid Them in the Square Root of -55

When dealing with square roots of negative numbers, common mistakes include ignoring the imaginary unit or misapplying real-number methods. Here are some tips to avoid these errors:

Mistake 1

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Forgetting about the Imaginary Unit

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Always remember that the square root of a negative number involves the imaginary unit 'i'.

For instance, the square root of -55 should be expressed as √55 * i, not just √55.

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Square Root of -55 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the magnitude of a complex number if one of its components is √(-55)?

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The magnitude is 55.317.

Explanation

The magnitude of a complex number a + bi is √(a² + b²).

Here, b = √55i = 7.416i.

Thus, the magnitude is √(0² + 7.416²) = √55 ≈ 7.416.

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Max, the Girl Character from BrightChamps

Problem 2

A signal oscillates with a frequency component of √(-55) Hz. What is the real magnitude of this component?

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The real magnitude is 7.416 Hz.

Explanation

The frequency component is given by √(-55) Hz, which is an imaginary number.

The real magnitude is the absolute value of √55, which is approximately 7.416 Hz.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate the product of √(-55) and 3.

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The product is 22.248i.

Explanation

First, find the square root of 55, which is approximately 7.416.

Then, multiply it by 3: 3 * 7.416i = 22.248i.

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Max, the Girl Character from BrightChamps

Problem 4

What is the result of squaring √(-55)?

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The result is -55.

Explanation

When you square √(-55), you get (√(-55))² = -55.

This is because squaring the square root of a number returns the original number.

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FAQ on Square Root of -55

1.What is √(-55) in its simplest form?

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2.What are the real and imaginary parts of √(-55)?

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

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4.Is 55 a perfect square?

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5.How is the imaginary unit 'i' defined?

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

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7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of -55?

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8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of -55?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -55

  • Square root: The square root is the inverse operation of squaring a number. In the context of negative numbers, it involves imaginary numbers.
     
  • Imaginary number: A number that can be written as a real number multiplied by the imaginary unit 'i', where i² = -1.
     
  • Complex number: A number consisting of a real part and an imaginary part, typically expressed in the form a + bi.
     
  • Magnitude: The magnitude of a complex number is the distance from the origin in the complex plane, calculated as √(a² + b²) for a complex number a + bi.
     
  • Absolute value: The non-negative value of a number without regard to its sign, for real numbers, or its distance from the origin, for complex numbers.
Professor Greenline from BrightChamps

About BrightChamps in Saudi Arabia

At BrightChamps, we recognize algebra as more than just symbols—it’s a key to unlock countless opportunities! Our goal is to help children across Saudi Arabia gain important math skills, focusing today on the Square Root of -55 with special attention to square roots—in a way that’s engaging, lively, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Riyadh’s Al Hokair Land, following scores at local football matches, or managing their allowance for the latest gadgets, mastering algebra boosts their confidence for daily challenges. Our interactive lessons make learning accessible and fun. Since children in Saudi Arabia learn in different ways, we tailor lessons to suit each learner. From Riyadh’s bustling streets to Jeddah’s historic landmarks, BrightChamps brings math to life, making it exciting and relevant all over Saudi Arabia. Let’s make square roots a fun part of every child’s math adventure!
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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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