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Last updated on May 26th, 2025

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Square Root of -50

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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 -50.

Square Root of -50 for US Students
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What is the Square Root of -50?

The square root is the inverse of the square of the number. The number -50 is a negative number, and its square root is not defined in the real number system. However, it can be expressed in terms of imaginary numbers. The square root of -50 is expressed as √(-50) = √(50) * i = 5√2 * i, where i is the imaginary unit satisfying i² = -1.

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Finding the Square Root of -50

The square root of a negative number involves imaginary numbers. Instead of using methods for perfect squares, we express the square root of negative numbers in terms of the imaginary unit i. Let us learn how to express the square root of -50:

 

Step 1: Factor the number 50 as 2 x 5 x 5.

 

Step 2: Since -50 is negative, express it as -1 x 50.

 

Step 3: The square root of -50 is then √(-1) * √(50).

 

Step 4: Simplify to get √(-50) = i * 5√2.

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Square Root of -50 by Prime Factorization

The prime factorization of 50 is 2 x 5 x 5. Since -50 is negative, we include the imaginary unit i:

 

Step 1: Prime factorize 50 as 2 x 5².

 

Step 2: Express -50 as -1 x 2 x 5².

 

Step 3: The square root of -50 is √(-1) * √(2) * √(5²).

 

Step 4: Simplify to get √(-50) = i * 5√2.

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Square Root of -50 by Approximation

Since the square root of -50 involves an imaginary number, we focus on approximating the real part, √50:

 

Step 1: Find the closest perfect squares around 50, which are 49 and 64.

 

Step 2: √50 is between √49 (7) and √64 (8).

 

Step 3: Use approximation to find √50 ≈ 7.07.

 

Therefore, the square root of -50 is approximately 7.07i.

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Common Mistakes and How to Avoid Them in the Square Root of -50

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

Mistake 1

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Ignoring the Imaginary Unit

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It is essential to remember that the square root of a negative number involves the imaginary unit.

For example, √(-50) should be expressed as 5√2i, not just 5√2.

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Square Root of -50 Examples

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Problem 1

Can you find the square root of -20?

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The square root of -20 is 2√5i.

Explanation

First, factor 20 as 2 x 2 x 5.

The square root of -20 is √(-1) * √(20) = i * 2√5, hence 2√5i.

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Problem 2

What is the square root of -36?

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The square root of -36 is 6i.

Explanation

Since 36 is a perfect square, its square root is 6.

Therefore, √(-36) = √(-1) * √(36) = 6i.

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Problem 3

Calculate 3 times the square root of -50.

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3 times the square root of -50 is 15√2i.

Explanation

The square root of -50 is 5√2i.

Multiply by 3 to get 15√2i.

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Problem 4

If the side length of a square is √(-81), what is its area?

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The area is -81 square units.

Explanation

The side length is √(-81) = 9i.

The area = (9i)² = -81.

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Problem 5

Express the product of √(-4) and √(-9).

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The product is 6.

Explanation

√(-4) = 2i and √(-9) = 3i.

The product is (2i) * (3i) = 6i² = -6.

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FAQ on Square Root of -50

1.What is √(-50) in its simplest form?

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2.What is the imaginary unit?

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

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4.How to simplify √(-100)?

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5.Why is i used in square roots of negative 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 -50?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of -50?

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

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Important Glossaries for the Square Root of -50

  • Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4.
     
  • Imaginary number: An imaginary number is a number that can be written as a real number multiplied by the imaginary unit i.
     
  • Imaginary unit: The imaginary unit is denoted by i, defined as √(-1), and is used to express the square root of negative numbers.
     
  • Complex number: A complex number consists of a real part and an imaginary part, represented as a + bi.
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.
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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 -50, 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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