Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of -49.
The square root is the inverse of the square of a number. Since -49 is a negative number, its square root involves imaginary numbers. The square root of -49 is expressed as √(-49) and can be written using the imaginary unit 'i', where i = √(-1). Thus, the square root of -49 is 7i.
The square root of a negative number involves imaginary numbers. The square root of -49 is not a real number, and the methods used for real numbers do not apply directly. Instead, we utilize the concept of imaginary numbers.
When dealing with the square root of negative numbers, we use the imaginary unit 'i', defined as √(-1). For -49, we have:
Step 1: Recognize -49 as 49 multiplied by -1.
Step 2: Apply the property of square roots: √(-49) = √(49) * √(-1).
Step 3: Calculate √(49), which is 7, and use the definition of i: √(-1) = i.
Step 4: Combine these results to get 7i.
Imaginary numbers are used to represent the square roots of negative numbers. The imaginary unit 'i' is the cornerstone of this concept, allowing us to calculate and understand values like √(-49). Imaginary numbers extend the real number system to form the complex number system.
Imaginary numbers have applications in various fields, such as engineering, physics, and computer science. They are essential in solving equations that do not have real solutions and are used in signal processing, control systems, and complex analysis.
Understanding the square root of negative numbers can be tricky. Students often make mistakes such as ignoring the imaginary unit 'i' or misapplying real number methods. Let's explore some common errors and how to avoid them.
What is the product of the square root of -49 and 3?
21i
The square root of -49 is 7i.
To find the product with 3, multiply 7i by 3: 7i × 3 = 21i.
Calculate the square of the square root of -49.
-49
The square root of -49 is 7i.
The square of 7i is (7i)² = 49 × i² = 49 × (-1) = -49.
If x = √(-49), what is x²?
-49
Since x = √(-49) = 7i, then x² = (7i)² = 49 × i² = 49 × (-1) = -49.
Find the result of multiplying √(-49) by 2i.
-14
The square root of -49 is 7i.
Multiplying by 2i gives: 7i × 2i = 14i² = 14 × (-1) = -14.
What is the square root of -49 plus the square root of 49?
0
The square root of -49 is 7i, and the square root of 49 is 7.
Adding these gives 7i + 7.
However, since they are not like terms, the expression remains as 7 + 7i.
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.
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