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Last updated on May 26th, 2025

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Square Root of -91

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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of -91.

Square Root of -91 for US Students
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What is the Square Root of -91?

The square root is the inverse of the square of the number. Since -91 is a negative number, it does not have a real number square root. In the context of complex numbers, the square root of -91 can be expressed using the imaginary unit 'i'. The square root of -91 is expressed as √(-91) = √91 * i, which is approximately 9.5394i, an imaginary number.

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Finding the Square Root of -91

The prime factorization method, long division method, and approximation method are typically used for real numbers. However, since -91 is negative, these methods do not directly apply. Instead, we can express the square root in terms of imaginary numbers.

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Square Root of -91 by Imaginary Numbers

To find the square root of a negative number, we incorporate the imaginary unit 'i', where i = √(-1).

 

Step 1: We express the square root of -91 as √(-91) = √91 * √(-1).

 

Step 2: Since √(-1) = i, we have √(-91) = √91 * i.

 

Step 3: Calculate √91, which is approximately 9.5394.

 

Step 4: The square root of -91 is then approximately 9.5394i, an imaginary number.

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Common Mistakes when Dealing with Square Roots of Negative Numbers

When working with square roots of negative numbers, it's essential to understand the role of the imaginary unit 'i' and not to apply real number methods directly.

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Understanding the Properties of Imaginary Numbers

Imaginary numbers are essential when dealing with square roots of negative numbers. The key property is that i² = -1, and this helps in simplifying expressions involving square roots of negative numbers.

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Common Mistakes and How to Avoid Them in the Square Root of -91

Students often make mistakes when dealing with square roots of negative numbers, such as ignoring the imaginary unit or incorrectly applying real number methods. Here are some common mistakes and how to avoid them.

Mistake 1

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Forgetting the Imaginary Unit 'i'

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When calculating the square root of a negative number, it is crucial to include the imaginary unit 'i'.

 

For example, forgetting to write √(-91) as 9.5394i can lead to incorrect conclusions.

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Square Root of -91 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the square root of -64 using imaginary numbers?

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The square root of -64 is ±8i.

Explanation

To find the square root of -64, express it as √(-64) = √64 * √(-1). Since √64 = 8 and √(-1) = i, the square root of -64 is ±8i.

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Problem 2

A field has an area of -91 square meters. What is the side length if measured using imaginary numbers?

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The side length is approximately ±9.5394i meters.

Explanation

The side length of a square field with an area -91 square meters can be found by taking the square root of -91, which is approximately ±9.5394i meters.

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Problem 3

Calculate √(-91) * 3 using imaginary numbers.

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The result is approximately ±28.6182i.

Explanation

First, find the square root of -91, which is approximately ±9.5394i. Multiply this by 3 to get ±28.6182i.

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Problem 4

What is the product of √(-25) and √(-4)?

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The product is ±10i² or ±(-10).

Explanation

First, find the square roots: √(-25) = ±5i and √(-4) = ±2i. Multiply them to get ±10i². Since i² = -1, the result is ±(-10).

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Problem 5

If the width of a rectangular field is √(-49)i meters, and the length is 14 meters, what is the perimeter?

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The perimeter is not a real number, but it includes imaginary components.

Explanation

The perimeter formula is 2 * (length + width). Using the imaginary width: 2 * (14 + 7i) = 28 + 14i. The perimeter includes an imaginary component.

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FAQ on Square Root of -91

1.What is √(-91) in terms of imaginary numbers?

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

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3.What is the imaginary unit 'i'?

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4.How do you express the square root of a negative number?

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5.What are complex numbers?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of -91?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of -91?

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

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About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of -91, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting 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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