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Last updated on May 26th, 2025

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Square Root of -162

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The square root is the inverse of the square of a number. When dealing with negative numbers, square roots become complex numbers. Here, we will discuss the square root of -162.

Square Root of -162 for Indian Students
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What is the Square Root of -162?

The square root of a negative number involves complex numbers. The square root of -162 is expressed in both radical and exponential form involving the imaginary unit i. In radical form, it is expressed as √-162 = √162 × i, whereas in exponential form as (162)^(1/2) × i. The value of √162 is approximately 12.7279, making the square root of -162 approximately 12.7279i, which is a complex number.

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Finding the Square Root of -162

To find the square root of a negative number, we need to use the concept of imaginary numbers. Let's explore the methods used to calculate the square root of -162:

 

1. Split into real and imaginary parts

 

2. Simplify the square root of the positive part

 

3. Combine with the imaginary unit i

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Square Root of -162: Step-by-Step Method

To find the square root of -162, we follow these steps:

 

Step 1: Recognize that -162 can be rewritten as (-1) × 162.

 

Step 2: The square root of -162 becomes √(-1) × √162.

 

Step 3: The square root of -1 is i (the imaginary unit).

 

Step 4: Calculate √162, which is approximately 12.7279.

 

Step 5: Multiply √162 by i to get the square root of -162 as approximately 12.7279i.

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Approximating the Square Root of 162

The approximation method for finding the square roots of a positive number can be applied here to find the real part of the complex square root.

 

Step 1: Identify the closest perfect squares around 162. They are 144 (12^2) and 169 (13^2).

 

Step 2: Use linear interpolation to estimate √162. (162 - 144) / (169 - 144) = 0.72

 

Step 3: Calculate 12 + 0.72 = 12.72

 

Thus, √162 is approximately 12.7279, and the square root of -162 is 12.7279i.

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Common Mistakes and How to Avoid Them in the Square Root of -162

When dealing with negative square roots, it's easy to make mistakes by not accounting for the imaginary unit or by misapplying methods suitable for real numbers. Let's look at some common errors and how to prevent them.

Mistake 1

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Ignoring the Imaginary Unit

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A common mistake is to forget the imaginary unit i when computing the square root of a negative number. The square root of -1 is not 1 but i. Hence, √-162 should be 12.7279i, not simply 12.7279.

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Square Root of -162 Examples

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Problem 1

Can you find the square root of -98 and explain it?

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The square root is approximately 9.899i.

Explanation

To find the square root of -98, split it as √(-1) × √98.

The square root of -1 is i, and √98 is approximately 9.899.

Thus, the square root of -98 is 9.899i.

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Problem 2

If the length of a side of a square is √-50, what is the area of the square?

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The area is -50 square units.

Explanation

The area of the square = side^2.

If the side length is √-50, the area = (√-50) * (√-50) = -50 square units.

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Problem 3

Calculate √-200 × 3.

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Approximately 42.4264i.

Explanation

First, find the square root of -200, which is approximately 14.1421i.

Then, multiply by 3: 14.1421i × 3 = 42.4264i.

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Problem 4

What is the square root of (-64 - 36)?

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The square root is 10i.

Explanation

First, find the sum of (-64 - 36), which is -100.

The square root of -100 = √(-1) × √100 = 10i.

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Problem 5

If a rectangle's dimensions are √-162 by 10, what is its area?

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The area is -1620 square units.

Explanation

The area of a rectangle = length × width.

With dimensions √-162 and 10, the area = (√-162) * 10 = -1620 square units.

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FAQ on Square Root of -162

1.What is √-162 in its simplest form?

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2.Is there a real number that is the square root of -162?

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3.What is the square of 162?

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4.What is the imaginary unit i?

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5.Can the square root of a negative number be graphed on the real number line?

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

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7.How can cultural or local activities in India support learning Algebra topics such as Square Root of -162?

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8.How do technology and digital tools in India support learning Algebra and Square Root of -162?

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

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Important Glossaries for the Square Root of -162

  • Imaginary Unit: The imaginary unit i is defined as √(-1), and is used to express square roots of negative numbers.

 

  • Complex Number: A number that includes both a real part and an imaginary part, expressed in the form a + bi.

 

  • Square Root: The square root of a number x is a value that, when multiplied by itself, gives the number x.

 

  • Perfect Square: A number that is the square of an integer.

 

  • Interpolation: A method used to estimate values between two known values.
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About BrightChamps in India

At BrightChamps, we see algebra as more than just symbols—it opens doors to endless opportunities! Our mission is to help children all over India develop vital math skills, focusing today on the Square Root of -162 with special attention to understanding square roots—in a way that’s engaging, lively, and easy to follow. Whether your child is calculating the speed of a passing train, keeping scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence needed for everyday situations. Our interactive lessons keep learning simple and fun. As kids in India have varied learning styles, we personalize our approach to match each child. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps brings math to life, making it relatable and exciting throughout India. 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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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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