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Last updated on May 26th, 2025

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Square Root of -62

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When a number is multiplied by itself, the result is called a square. The inverse operation is finding the square root. Square roots are used in fields like engineering, physics, and mathematics. Here, we will discuss the square root of -62.

Square Root of -62 for Thai Students
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What is the Square Root of -62?

The square root is the inverse of squaring a number. Since -62 is a negative number, it does not have a real square root. In the complex number system, the square root of -62 is expressed as an imaginary number. It can be written as √-62 = √62 * i, where i is the imaginary unit defined as √-1. Therefore, the square root of -62 is √62 * i, which is a complex number.

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Finding the Square Root of -62

Since -62 is negative, the methods used for real numbers like approximation or long division won't apply directly. Instead, we consider the square root in terms of complex numbers. Let's discuss the concept behind finding the square root of a negative number:

 

  • Imaginary unit (i): The imaginary unit is defined as √-1 and is denoted by i.
  • Complex form: The square root of a negative number can be expressed using i. For -62, the square root is √62 * i.
Professor Greenline from BrightChamps

Square Root of -62 by Prime Factorization

Prime factorization is not applicable to finding the square root of a negative number using real number methods. Instead, the focus is on expressing the number in terms of i. Since 62 is not a perfect square, we can't pair prime factors as with positive numbers. Thus, the square root of -62 in terms of complex numbers is √62 * i.

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Square Root of -62 by Long Division Method

The long division method is used for finding the square root of positive numbers. Because -62 is negative, we don't use this method directly. Instead, we express the square root of -62 as √62 * i, where √62 is determined using approximation or other methods for positive 62, and i represents the imaginary unit.

Professor Greenline from BrightChamps

Square Root of -62 by Approximation Method

Approximation methods for estimating square roots apply to positive numbers. For -62, we find the square root of the positive counterpart: 62. Then, we express it in terms of complex numbers. Let's consider: 1. √62 is approximately 7.874. 2. The square root of -62 is √62 * i, or approximately 7.874i.

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Common Mistakes and How to Avoid Them in the Square Root of -62

Students often make errors when dealing with square roots of negative numbers, such as ignoring the imaginary unit i or misapplying methods for real numbers. Let's explore some common mistakes:

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 i. Failing to include i when finding the square root of -62 will result in an incorrect answer.

For example, forgetting that √-62 = √62 * i leads to mistakes.

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Square Root of -62 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √-62?

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The area cannot be calculated using real numbers.

Explanation

The side length √-62 is imaginary, represented as √62 * i.

Since area requires real numbers, it cannot be computed with imaginary lengths.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring -62 square feet is built; if each of the sides is √-62, what will be the square feet of half of the building?

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Impossible to determine in real terms.

Explanation

The area being negative and side length imaginary indicates a non-physical scenario, hence real area cannot be computed.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √-62 × 5.

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39.37i

Explanation

First, find the square root of 62, approximately 7.874.

Then, multiply by i and 5: 7.874i × 5 = 39.37i.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (-62 + 20)?

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Cannot be determined directly.

Explanation

The expression involves both negative and positive parts, and requires complex number handling.

The real component affects results.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √-62 units and width ‘w’ is 38 units.

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Cannot compute with imaginary length.

Explanation

With an imaginary length of √-62, real-world calculations for perimeter aren't possible, as perimeter requires real values.

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FAQ on Square Root of -62

1.What is √-62 in its simplest form?

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2.What is the real square root of 62?

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3.Can √-62 be expressed as a real number?

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4.Is 62 a perfect square?

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5.What does the imaginary unit i represent?

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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 -62?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of -62?

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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 -62

  • Imaginary Unit: Denoted as i, it is defined as the square root of -1 and is used to express square roots of negative numbers.
     
  • Complex Number: A number that has both a real part and an imaginary part, often expressed in the form a + bi.
     
  • Negative Number: A real number less than zero, represented with a minus sign.
     
  • Approximation: Estimating a value based on nearby known or calculated values.
     
  • Real Number: A value representing a quantity along a continuous line, including both rational and irrational numbers.
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 -62 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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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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