Square Root of -73
2026-02-28 13:21 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-minus-73

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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 square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of -73.

What is 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.

Finding the Square Root of -73

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:

  • Imaginary number concept

Square Root of -73 Using Imaginary Number Concept

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.

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Square Root of -73 by Approximation Method

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 and Their Importance

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.

Common Mistakes and How to Avoid Them in the Square Root of -73

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.

Problem 1

Can you help Max find the expression of the square root of -50?

Okay, lets begin

The expression is 5√2 * i.

Explanation

The square root of -50 is expressed as √(-50) = √(50) * √(-1) = √(25 * 2) * i = 5√2 * i.

Well explained 👍

Problem 2

If a complex number z is defined as z = √(-73) + 5, what is the imaginary part of z?

Okay, lets begin

The imaginary part is approximately 8.5.

Explanation

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.

Well explained 👍

Problem 3

Calculate 2 * √(-73).

Okay, lets begin

Approximately 17i.

Explanation

First, determine √(-73) = √73 * i.

Approximating √73 as 8.5, we have 2 * 8.5 * i = 17i.

Well explained 👍

Problem 4

What will be the square root of (-36)?

Okay, lets begin

The square root is 6i.

Explanation

To find the square root, express √(-36) as √(36) * √(-1) = 6 * i.

Therefore, the square root of (-36) is ±6i.

Well explained 👍

Problem 5

If a rectangle has a length of √(-49) and a width of 5, what is the area in terms of i?

Okay, lets begin

The area is 35i square units.

Explanation

Area of the rectangle = length * width.

The length is √(-49) = 7i.

Thus, the area = 7i * 5 = 35i square units.

Well explained 👍

FAQ on Square Root of -73

1.What is √(-73) in its simplest form?

The simplest form of √(-73) is √73 * i, where 'i' is the imaginary unit.

2.What is the imaginary unit?

The imaginary unit 'i' is defined as the square root of -1, and it is used to express the square roots of negative numbers.

3.Why can't negative numbers have real square roots?

Negative numbers cannot have real square roots because the square of any real number is non-negative. Thus, a negative number does not have a real square root.

4.Can we approximate √(-73)?

Yes, you can approximate √73 as 8.5. Therefore, √(-73) can be approximated as 8.5i.

5.How are imaginary numbers used in engineering?

Imaginary numbers are used in engineering to analyze electrical circuits, control systems, and signal processing, among other applications.

Important Glossaries for the Square Root of -73

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, it involves imaginary numbers.
     
  • Imaginary number: A number that can be written as a real number multiplied by the imaginary unit 'i', where i is the square root of -1.
     
  • Complex number: A number that has both a real part and an imaginary part, expressed in the form a + bi.
     
  • Radical: An expression that includes a root symbol (√) and represents the root of a number.
     
  • Approximation: The process of estimating a number by finding a close but not exact value, often used for non-perfect squares.

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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.