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Last updated on May 26th, 2025

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Square Root of -20

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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 concept of square roots extends to complex numbers when dealing with negative numbers. Here, we will discuss the square root of -20.

Square Root of -20 for US Students
Professor Greenline from BrightChamps

What is the Square Root of -20?

The square root is the inverse of the square of the number. Since -20 is a negative number, its square root is not a real number. Instead, it is expressed in terms of imaginary numbers. The square root of -20 can be written as √(-20) = √(20) × √(-1). We know that √(-1) is represented by the imaginary unit 'i'. Therefore, √(-20) = √20 × i = 4.4721i, which is an imaginary number.

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Finding the Square Root of -20

For negative numbers, the square root involves imaginary numbers. The process involves finding the square root of the absolute value first, and then multiplying by 'i'. Let us now explore how this is done:

 

Find the square root of 20.

Multiply the result by 'i' to account for the negative sign.

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Square Root of -20 by Prime Factorization Method

The prime factorization of the absolute value 20 is considered here. Let us break down 20 into its prime factors:

 

Step 1: Finding the prime factors of 20. Breaking it down, we get 2 × 2 × 5: 2² × 5¹

 

Step 2: Now we have the prime factors of 20. The square root of 20 is √(2² × 5) = 2√5. Since we need the square root of -20, we multiply by 'i': √(-20) = 2√5 × i = 4.4721i

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Square Root of -20 by Long Division Method

The long division method is used to find the square root of non-negative numbers and can be applied to the absolute value of -20. We then introduce 'i' for the negative sign. Here is the step-by-step process:

 

Step 1: Begin by finding the square root of 20 using long division.

 

Step 2: Apply the long division steps to approximate √20, which results in about 4.4721. Step 3: Since we need the square root of -20, multiply the result by 'i': √(-20) = 4.4721i

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Square Root of -20 by Approximation Method

Approximation method involves estimating the square root of the absolute value 20 and then introducing 'i'. Follow these steps:

 

Step 1: Identify the closest perfect squares around 20, which are 16 and 25.

 

Step 2: Use the approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (20 - 16) / (25 - 16) = 4 / 9 ≈ 0.444

 

Step 3: The approximate square root of 20 is 4 + 0.444 = 4.444.

 

Step 4: Multiply by 'i' to get the square root of -20: √(-20) ≈ 4.444i

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Common Mistakes and How to Avoid Them in the Square Root of -20

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

Mistake 1

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Forgetting about the imaginary unit 'i'

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When dealing with square roots of negative numbers, it's crucial to include 'i' in the solution.

 

For example, forgetting to write 'i' in √(-20) leads to an incorrect answer. Always remember that √(-1) is 'i'.

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Square root of -20 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the imaginary part of a number if its value is √(-25)?

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The imaginary part is 5i.

Explanation

The square root of -25 can be expressed as √(25) × √(-1) = 5 × i = 5i. Therefore, the imaginary part is 5i.

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Max, the Girl Character from BrightChamps

Problem 2

A complex number is given as 4 + √(-36). What is the magnitude of this complex number?

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The magnitude is 10.

Explanation

The square root of -36 is 6i.

The complex number is 4 + 6i.

The magnitude is calculated as √(4² + 6²) = √(16 + 36) = √52 = 7.2111, approximately 10 after correct approximation.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate 3 times the square root of -45.

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The result is 9i√5.

Explanation

First, find the square root of -45: √(-45) = √(45) × i = 3√5 × i. Then multiply by 3: 3 × (3√5 × i) = 9i√5.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (-64)?

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The square root is 8i.

Explanation

To find the square root, consider √(-64) = √(64) × √(-1) = 8 × i = 8i. Therefore, the square root of (-64) is ±8i.

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Max, the Girl Character from BrightChamps

Problem 5

Find the sum of the square root of -9 and the square root of -16.

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The sum is 7i.

Explanation

The square root of -9 is 3i and the square root of -16 is 4i. Adding these gives 3i + 4i = 7i.

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FAQ on Square Root of -20

1.What is √(-20) in its simplest form?

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2.What is the imaginary unit 'i'?

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3.Calculate the square of -20.

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4.Is -20 a perfect square?

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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 -20?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of -20?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of -20

  • Imaginary number: An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i² = -1.

 

  • Complex number: A complex number is a number that has both a real and an imaginary part, usually expressed in the form a + bi.

 

  • Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Negative numbers have imaginary square roots.

 

  • Magnitude: The magnitude of a complex number a + bi is given by √(a² + b²).

 

  • Approximation: The process of finding a value close to the actual value, useful when exact values are difficult to calculate.
Professor Greenline from BrightChamps

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 -20, 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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