Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering and physics. Here, we will discuss the square root of -55.
The square root is the inverse of squaring a number. When dealing with negative numbers, the square root involves imaginary numbers, as no real number squared results in a negative. The square root of -55 is expressed using the imaginary unit 'i'. In standard form, it is written as √(-55) = √55 * i, which is an imaginary number.
Since -55 is a negative number, its square root involves imaginary numbers. We cannot use the typical real-number methods like the prime factorization or long division to find the square root. Instead, we use the concept of imaginary numbers. Let us examine the following approach:
The square root of a negative number is expressed using the imaginary unit 'i', where i² = -1. Therefore, to find √(-55), we express it as √(55) * i. Calculating √55 involves finding the square root of the positive part:
Step 1: Approximate the square root of 55. √55 ≈ 7.416
Step 2: Combine with the imaginary unit. √(-55) = 7.416i
When dealing with square roots of negative numbers, common mistakes include ignoring the imaginary unit or misapplying real-number methods. Here are some tips to avoid these errors:
Can you help Max find the magnitude of a complex number if one of its components is √(-55)?
The magnitude is 55.317.
The magnitude of a complex number a + bi is √(a² + b²).
Here, b = √55i = 7.416i.
Thus, the magnitude is √(0² + 7.416²) = √55 ≈ 7.416.
A signal oscillates with a frequency component of √(-55) Hz. What is the real magnitude of this component?
The real magnitude is 7.416 Hz.
The frequency component is given by √(-55) Hz, which is an imaginary number.
The real magnitude is the absolute value of √55, which is approximately 7.416 Hz.
Calculate the product of √(-55) and 3.
The product is 22.248i.
First, find the square root of 55, which is approximately 7.416.
Then, multiply it by 3: 3 * 7.416i = 22.248i.
What is the result of squaring √(-55)?
The result is -55.
When you square √(-55), you get (√(-55))² = -55.
This is because squaring the square root of a number returns the original number.
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.
: He loves to play the quiz with kids through algebra to make kids love it.