Square Root of -63
2026-02-28 10:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-minus-63

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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. Square roots are used in various fields like physics, engineering, and computer graphics. Here, we will discuss the square root of -63.

What is the Square Root of -63?

The square root is the inverse operation of squaring a number. Since -63 is negative, it does not have a real square root. In mathematics, the square root of a negative number is expressed using the imaginary unit 'i', where i² = -1. Therefore, the square root of -63 is expressed as √-63 = √63 * i or approximately 7.937 * i, which is a complex number.

Understanding Imaginary Numbers

The concept of imaginary numbers is used to denote the square roots of negative numbers. The imaginary unit 'i' is defined such that i² = -1. Therefore, the square root of -63 can be written as: √-63 = √63 * i The value √63 is approximately 7.937.

Thus, the square root of -63 is written as 7.937 * i.

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Expressing Complex Numbers

Complex numbers consist of a real part and an imaginary part. Here, since we are finding the square root of a negative number, the result is purely imaginary with no real component.

Thus, the square root of -63 is a complex number expressed as: √-63 = 0 + 7.937 * i

Applications of Imaginary Numbers

Imaginary numbers, though not real, have practical applications in various fields. They are used in electrical engineering to describe the behavior of currents and voltages, in signal processing, and in solving equations that describe wave behaviors. Understanding and expressing square roots of negative numbers is vital in these fields.

Common Mistakes and How to Avoid Them with Square Roots of Negative Numbers

Students may struggle with square roots of negative numbers, often neglecting the imaginary component. Let's examine common mistakes and how to address them.

Problem 1

Can you find the square root of -49?

Okay, lets begin

The square root is 7i.

Explanation

Since -49 is negative, its square root involves 'i'.

The square root of 49 is 7, so the square root of -49 is 7i.

Well explained 👍

Problem 2

What is the square of the imaginary unit 'i'?

Okay, lets begin

The square is -1.

Explanation

By definition, i² = -1.

This is a fundamental property of the imaginary unit.

Well explained 👍

Problem 3

Calculate 3 times the square root of -9.

Okay, lets begin

The result is 9i.

Explanation

The square root of -9 is 3i.

Multiplying by 3 gives 9i.

Well explained 👍

Problem 4

What is the sum of the square roots of -16 and -25?

Okay, lets begin

The sum is 7i.

Explanation

The square root of -16 is 4i, and the square root of -25 is 5i.

Adding these gives 9i.

Well explained 👍

Problem 5

Find the square root of -81.

Okay, lets begin

The square root is 9i.

Explanation

The square root of 81 is 9, so the square root of -81 is 9i.

Well explained 👍

FAQ on Square Root of -63

1.What is √-63 in its simplest form?

The simplest form of √-63 is √63 * i, where i is the imaginary unit.

2.Can negative numbers have real square roots?

No, negative numbers do not have real square roots. Their square roots are imaginary numbers.

3.What does the imaginary unit 'i' represent?

The imaginary unit 'i' is defined such that i² = -1. It is used to represent square roots of negative numbers.

4.Are there any real applications of imaginary numbers?

Yes, imaginary numbers are used in electrical engineering, control systems, signal processing, and quantum physics, among other fields.

5.How can I express the square root of -100?

The square root of -100 is 10i, as the square root of 100 is 10.

Important Glossaries for the Square Root of -63

  • Imaginary unit: The imaginary unit 'i' is defined as √-1. It is used to express the square roots of negative numbers.
     
  • Complex number: A complex number has a real part and an imaginary part, typically written as a + bi.
     
  • Imaginary number: A number that can be written as a real number multiplied by the imaginary unit 'i'. For example, 3i is an imaginary number.
     
  • Complex plane: A plane used to represent complex numbers graphically, with the horizontal axis representing the real part and the vertical axis representing the imaginary part.
     
  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, the result involves imaginary numbers.

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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.