Last updated on May 26th, 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 square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of -36.
The square root is the inverse of the square of a number. The square root of -36 is not a real number because negative numbers do not have real square roots. Instead, it is expressed in terms of imaginary numbers. The square root of -36 is ±6i, where 'i' is the imaginary unit and i² = -1.
To understand the square root of -36, we use the concept of imaginary numbers. Imaginary numbers are used when dealing with the square roots of negative numbers. Since -36 is negative, its square root is expressed as an imaginary number.
The imaginary unit 'i' is defined such that i² = -1. Therefore, the square root of -36 can be expressed as √(-36) = √(36) × √(-1) = 6i. Both +6i and -6i are solutions, as squaring either will return -36.
Imaginary numbers, including the square root of negative numbers, are used in various fields such as electrical engineering, signal processing, and quantum physics. They help in solving equations that do not have real solutions.
While dealing with imaginary numbers, it's crucial to remember that they are not real numbers and cannot be placed on the traditional number line. Also, confusing the imaginary unit 'i' with real numbers or misplacing it in calculations can lead to errors.
Students make mistakes when calculating the square root of negative numbers, often forgetting the use of the imaginary unit 'i'. Here are a few common mistakes students make and how to avoid them.
Calculate the square of 3i.
-9
To find the square of 3i, use (3i)² = 9(i²) = 9(-1) = -9.
If x = √(-81), what is x²?
-81
Since x = √(-81) = 9i, then x² = (9i)² = 81(i²) = 81(-1) = -81.
Is √(-25) a real number?
No
The square root of a negative number, like √(-25), is not a real number.
It is an imaginary number, expressed as 5i.
What is the product of 4i and 2i?
-8
The product of 4i and 2i is (4i)(2i) = 8(i²) = 8(-1) = -8.
Simplify i³.
-i
i³ = i² × i = (-1) × i = -i.
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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