Square Root of -50
2026-02-28 10:31 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-minus-50

226 Learners

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 -50.

What is the Square Root of -50?

The square root is the inverse of the square of the number. The number -50 is a negative number, and its square root is not defined in the real number system. However, it can be expressed in terms of imaginary numbers. The square root of -50 is expressed as √(-50) = √(50) * i = 5√2 * i, where i is the imaginary unit satisfying i² = -1.

Finding the Square Root of -50

The square root of a negative number involves imaginary numbers. Instead of using methods for perfect squares, we express the square root of negative numbers in terms of the imaginary unit i. Let us learn how to express the square root of -50:

Step 1: Factor the number 50 as 2 x 5 x 5.

Step 2: Since -50 is negative, express it as -1 x 50.

Step 3: The square root of -50 is then √(-1) * √(50).

Step 4: Simplify to get √(-50) = i * 5√2.

Square Root of -50 by Prime Factorization

The prime factorization of 50 is 2 x 5 x 5. Since -50 is negative, we include the imaginary unit i:

Step 1: Prime factorize 50 as 2 x 5².

Step 2: Express -50 as -1 x 2 x 5².

Step 3: The square root of -50 is √(-1) * √(2) * √(5²).

Step 4: Simplify to get √(-50) = i * 5√2.

Explore Our Programs

Square Root of -50 by Approximation

Since the square root of -50 involves an imaginary number, we focus on approximating the real part, √50:

Step 1: Find the closest perfect squares around 50, which are 49 and 64.

Step 2: √50 is between √49 (7) and √64 (8).

Step 3: Use approximation to find √50 ≈ 7.07.

Therefore, the square root of -50 is approximately 7.07i.

Common Mistakes and How to Avoid Them in the Square Root of -50

Students often make mistakes when dealing with square roots of negative numbers, such as ignoring the imaginary unit. Here are some common mistakes and how to avoid them.

Problem 1

Can you find the square root of -20?

Okay, lets begin

The square root of -20 is 2√5i.

Explanation

First, factor 20 as 2 x 2 x 5.

The square root of -20 is √(-1) * √(20) = i * 2√5, hence 2√5i.

Well explained 👍

Problem 2

What is the square root of -36?

Okay, lets begin

The square root of -36 is 6i.

Explanation

Since 36 is a perfect square, its square root is 6.

Therefore, √(-36) = √(-1) * √(36) = 6i.

Well explained 👍

Problem 3

Calculate 3 times the square root of -50.

Okay, lets begin

3 times the square root of -50 is 15√2i.

Explanation

The square root of -50 is 5√2i.

Multiply by 3 to get 15√2i.

Well explained 👍

Problem 4

If the side length of a square is √(-81), what is its area?

Okay, lets begin

The area is -81 square units.

Explanation

The side length is √(-81) = 9i.

The area = (9i)² = -81.

Well explained 👍

Problem 5

Express the product of √(-4) and √(-9).

Okay, lets begin

The product is 6.

Explanation

√(-4) = 2i and √(-9) = 3i.

The product is (2i) * (3i) = 6i² = -6.

Well explained 👍

FAQ on Square Root of -50

1.What is √(-50) in its simplest form?

The simplest form of √(-50) is 5√2i, where i is the imaginary unit.

2.What is the imaginary unit?

The imaginary unit i is defined as √(-1), satisfying i² = -1.

3.Can the square root of a negative number be real?

No, the square root of a negative number cannot be real; it involves the imaginary unit i.

4.How to simplify √(-100)?

Simplify √(-100) as √(-1) * √(100) = 10i.

5.Why is i used in square roots of negative numbers?

The imaginary unit i allows for the expression of square roots of negative numbers, as they are not defined in the real number system.

Important Glossaries for the Square Root of -50

  • Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4.
     
  • Imaginary number: An imaginary number is a number that can be written as a real number multiplied by the imaginary unit i.
     
  • Imaginary unit: The imaginary unit is denoted by i, defined as √(-1), and is used to express the square root of negative numbers.
     
  • Complex number: A complex number consists of a real part and an imaginary part, represented as a + bi.
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.