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Last updated on May 26th, 2025

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Square Root of -216

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When a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The concept of square roots extends to complex numbers when dealing with negative numbers. Here, we will delve into the square root of -216.

Square Root of -216 for Saudi Students
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What is the Square Root of -216?

The square root of a negative number involves complex numbers, as no real number squared equals a negative number. The square root of -216 is expressed using the imaginary unit 'i', where i² = -1. Thus, the square root of -216 is written as √(-216) = √216 * i, which simplifies to approximately 14.7i. This is because √216 is approximately 14.7, and multiplying by i gives the imaginary result.

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Finding the Square Root of -216

To find the square root of a negative number, we involve the imaginary unit 'i'. Let's explore the methods:

 

1. Expressing in terms of 'i'

 

2. Calculating the square root of the positive part

 

3. Combining with 'i'

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Square Root of -216 by Expressing in Terms of 'i'

The imaginary unit 'i' is used to represent the square root of negative numbers. For -216, the calculation is:

 

Step 1: Recognize that -216 can be expressed as 216 multiplied by -1.

 

Step 2: The square root of -216 is written as √(-216) = √(216) * √(-1).

 

Step 3: Since √(-1) = i, we have √(-216) = √(216) * i.

 

Step 4: Calculate √216. The approximate value is 14.7.

 

Step 5: Combine this with 'i' to get the result: 14.7i.

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Square Root of -216 by Calculating the Positive Part

Finding the square root of the positive part of -216 involves:

 

Step 1: Calculate the square root of 216. Using approximation or estimation, √216 ≈ 14.7.

 

Step 2: Use the imaginary unit to represent the negative aspect. So, √(-216) = 14.7i.

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Square Root of -216 by Combining with 'i'

Here’s how to combine the result with 'i':

 

Step 1: Recognize that √(-216) = √216 * i.

 

Step 2: Compute √216, which is approximately 14.7.

 

Step 3: Multiply 14.7 by 'i', giving the final square root of -216 as 14.7i.

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Common Mistakes and How to Avoid Them in the Square Root of -216

Mistakes often occur when students deal with negative square roots. It's important to remember the role of the imaginary unit 'i'. Here are some common errors to avoid:

Mistake 1

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Ignoring the Imaginary Unit 'i'

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A frequent mistake is treating the square root of a negative number as real. Always use 'i' for negative square roots.

For example, √(-9) should be 3i, not a real number.

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Square Root of -216 Examples

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Problem 1

What is the square root of -256?

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The square root is 16i.

Explanation

For -256, we first calculate √256 = 16.

Then, multiply by 'i' to account for the negative, resulting in 16i.

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Problem 2

How do you express the square root of -81?

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9i

Explanation

The square root of 81 is 9.

Combining with 'i', the square root of -81 is 9i.

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Problem 3

Calculate √(-49) x 3.

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The result is 21i.

Explanation

First, find the square root of -49, which is 7i.

Then multiply by 3 to get 21i.

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Problem 4

What is the square root of (-64 + 16)?

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The square root is 8i.

Explanation

First, simplify (-64 + 16) to -48.

Then, calculate √48 ≈ 6.93.

Finally, express it as 6.93i.

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Problem 5

If the length of a side of a square is √(-36), what is its area?

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The area is -36 square units.

Explanation

Since the side is 6i, the area is (6i)² = -36.

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FAQ on Square Root of -216

1.What is √(-216) in its simplest form?

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2.What are the factors of 216?

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3.Calculate the square of 216.

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4.Is -216 a prime number?

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5.What is the cube root of -216?

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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 -216?

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8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of -216?

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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 -216

  • Complex Number: A number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

 

  • Imaginary Unit 'i': Defined as the square root of -1, used to express the square roots of negative numbers.

 

  • Square Root: The square root of a number x is a number y such that y² = x. For negative numbers, it involves 'i'.

 

  • Irrational Number: A real number that cannot be expressed as a simple fraction. Square roots of non-perfect squares are often irrational.

 

  • Approximation: The process of finding a value that is close enough to the correct value, typically within an acceptable range of error.
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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 -216 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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