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 -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.
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.
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.
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.
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.
Can you find the square root of -20?
The square root of -20 is 2√5i.
First, factor 20 as 2 x 2 x 5.
The square root of -20 is √(-1) * √(20) = i * 2√5, hence 2√5i.
What is the square root of -36?
The square root of -36 is 6i.
Since 36 is a perfect square, its square root is 6.
Therefore, √(-36) = √(-1) * √(36) = 6i.
Calculate 3 times the square root of -50.
3 times the square root of -50 is 15√2i.
The square root of -50 is 5√2i.
Multiply by 3 to get 15√2i.
If the side length of a square is √(-81), what is its area?
The area is -81 square units.
The side length is √(-81) = 9i.
The area = (9i)² = -81.
Express the product of √(-4) and √(-9).
The product is 6.
√(-4) = 2i and √(-9) = 3i.
The product is (2i) * (3i) = 6i² = -6.
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.