Square Root of -2/3
2026-02-28 06:01 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-minus-2/3

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Last updated on August 5, 2025

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 into complex numbers when dealing with negative numbers. Here, we will discuss the square root of -2/3.

Finding the Square Root of -2/3

To find the square root of a negative fraction, we need to separate the negative sign and use the imaginary unit 'i'. We treat the positive part of the fraction separately from the negative sign. Let us now learn the following methods:

  • Expressing with imaginary numbers
     
  • Simplifying the fraction for square root calculation

Square Root of -2/3 by Expressing with Imaginary Numbers

The square root of a negative number is expressed using the imaginary unit 'i'. Let's look at how to express the square root of -2/3:

Step 1: Separate the negative sign and express it with 'i'. √(-2/3) = √(2/3) * i
 

Step 2: Calculate the square root of the positive fraction. √(2/3) can be written as √2/√3.
 

Step 3: Simplify the expression. √(-2/3) = (√2/√3) * i

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Simplifying the Expression √(2/3)

To simplify √(2/3), we can multiply both numerator and denominator by √3 to rationalize the denominator:

Step 1: Multiply by √3/√3: (√2/√3) * (√3/√3) = √6 / 3

Step 2: Express the square root of -2/3 using this result: √(-2/3) = (√6/3) * i

Applications of the Square Root of Negative Numbers

Square roots of negative numbers appear in various fields, especially in electrical engineering and signal processing, where the concept of complex numbers is used extensively. Understanding how to express and manipulate these numbers is critical for solving complex equations and modeling waveforms.

Common Mistakes and How to Avoid Them in the Square Root of -2/3

Students often make errors when dealing with square roots of negative numbers, such as forgetting to use the imaginary unit 'i' or incorrectly simplifying fractions. Let's examine some of these mistakes in detail.

Problem 1

How would you express the square root of -4/9 in terms of 'i'?

Okay, lets begin

The expression is (2/3) * i.

Explanation

The square root of -4/9 can be split into √(-1) * √(4/9). Therefore, it is √4/√9 * i, which simplifies to (2/3) * i.

Well explained 👍

Problem 2

Calculate the product of √(-2/3) and 3.

Okay, lets begin

The result is √6 * i.

Explanation

First, express √(-2/3) as (√6/3) * i. Multiply by 3: 3 * (√6/3) * i = √6 * i.

Well explained 👍

Problem 3

If you have a complex number represented as √(-2/3), what is its magnitude?

Okay, lets begin

The magnitude is √(2/3).

Explanation

The magnitude of a complex number a * i is |a|. Here, a = √(2/3), so the magnitude is √(2/3).

Well explained 👍

Problem 4

Explain how to find the square root of -1/4.

Okay, lets begin

The square root is (1/2) * i.

Explanation

Separate the negative: √(-1/4) = √(-1) * √(1/4). This becomes i * (1/2), or (1/2) * i.

Well explained 👍

Problem 5

What is the square of the square root of -2/3?

Okay, lets begin

The square is -2/3.

Explanation

Squaring √(-2/3) gives (-2/3) because (√(-2/3))² = -2/3.

Well explained 👍

FAQ on Square Root of -2/3

1.What is the simplest form of √(-2/3)?

The simplest form of √(-2/3) is (√6/3) * i, where 'i' represents the imaginary unit.

2.Why do we use 'i' for negative square roots?

'i' is used to represent the square root of -1, allowing us to write square roots of negative numbers as complex numbers.

3.What are complex numbers?

Complex numbers are numbers that include a real part and an imaginary part, typically written in the form a + bi.

4.Is √(-2/3) a real number?

No, √(-2/3) is not a real number; it is a complex number because it involves the imaginary unit 'i'.

5.How do you rationalize the denominator of √(2/3)?

To rationalize √(2/3), multiply by √3/√3 to get √6/3.

Important Glossaries for the Square Root of -2/3

  • Square root: The inverse operation of squaring a number. For negative numbers, this involves the imaginary unit 'i'.
  • Imaginary unit 'i': A mathematical concept used to represent the square root of -1, allowing for the expression of complex numbers.
  • Complex number: A number comprising a real part and an imaginary part, often written in the form a + bi.
  • Rationalization: The process of eliminating a square root from the denominator of a fraction.
  • Magnitude: The absolute value of a complex number, representing its size or length.

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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.

Fun Fact

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