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 the field of vehicle design, finance, etc. Here, we will discuss the square root of -73.
The square root is the inverse of the square of the number. The number -73 does not have a real square root because it is negative. However, it does have an imaginary square root. The square root of -73 can be expressed in both radical and exponential form with an imaginary unit. In radical form, it is expressed as √(-73), whereas (-73)^(1/2) in exponential form. The square root of -73 is an imaginary number because it involves the square root of a negative number, which is not defined in the set of real numbers.
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are typically used. However, for negative numbers, we use the concept of imaginary numbers. Let us explore the following methods:
For a negative number, the square root involves the imaginary unit 'i', which is defined as √(-1). Now, let's express the square root of -73:
Step 1: Recognize that -73 is negative.
Step 2: Express √(-73) as √(73) * √(-1).
Step 3: Simplify to get √73 * i.
Since 73 is not a perfect square, √73 remains as it is in its simplest radical form.
The approximation method can be used to find the square root of positive numbers, but here we apply it in terms of absolute value:
Step 1: Find the closest perfect squares to 73. The closest perfect square below 73 is 64, and the closest perfect square above 73 is 81. Hence, √73 falls between 8 and 9.
Step 2: Approximate √73 to be closer to 8.5 based on its position between 64 and 81.
Step 3: Since we are dealing with -73, the final expression is approximately 8.5i.
Imaginary numbers extend the concept of square roots to negative numbers. They are crucial in various fields such as electrical engineering, quantum physics, and applied mathematics. Understanding how to handle these numbers is essential for complex problem-solving.
Students often make mistakes while finding the square root, such as misunderstanding imaginary numbers or incorrectly simplifying radicals. Let's look at some of these common mistakes in detail.
Can you help Max find the expression of the square root of -50?
The expression is 5√2 * i.
The square root of -50 is expressed as √(-50) = √(50) * √(-1) = √(25 * 2) * i = 5√2 * i.
If a complex number z is defined as z = √(-73) + 5, what is the imaginary part of z?
The imaginary part is approximately 8.5.
The complex number z = √(-73) + 5 is broken down into real and imaginary parts.
The imaginary part is √73 * i, which is approximately 8.5i.
Hence, the imaginary part is approximately 8.5.
Calculate 2 * √(-73).
Approximately 17i.
First, determine √(-73) = √73 * i.
Approximating √73 as 8.5, we have 2 * 8.5 * i = 17i.
What will be the square root of (-36)?
The square root is 6i.
To find the square root, express √(-36) as √(36) * √(-1) = 6 * i.
Therefore, the square root of (-36) is ±6i.
If a rectangle has a length of √(-49) and a width of 5, what is the area in terms of i?
The area is 35i square units.
Area of the rectangle = length * width.
The length is √(-49) = 7i.
Thus, the area = 7i * 5 = 35i square units.
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.