Understanding the Problem: Negative 15 Square Root Divided by Negative Square Root 3
This mathematical expression might seem daunting at first glance, but it can be broken down into manageable steps. Let's unpack what we're dealing with and how to solve it.
What does "Negative 15 Square Root" mean?
The phrase "Negative 15 Square Root" implies we're calculating the square root of -15. Remember, the square root of a number is the value that, when multiplied by itself, equals the original number. However, there's a crucial detail here: we're dealing with a negative number.
The Role of Imaginary Numbers
When we encounter the square root of a negative number, we enter the realm of imaginary numbers. These are numbers represented by the symbol 'i', where i² = -1. The square root of -1 is denoted as 'i'.
Breaking down the Calculation
Let's break down the expression step-by-step:
- Square Root of -15: This is where our imaginary number comes into play. Since -15 is a negative number, its square root is expressed in terms of 'i'. We can rewrite it as √-15 = √(15 * -1) = √15 * √-1 = √15i.
- Negative Square Root of 3: This is the square root of 3 with a negative sign in front. The square root of 3 is an irrational number, meaning it can't be expressed as a simple fraction. We leave it as √3.
- Dividing: Now we have (√15i) / (-√3). To simplify, we can divide the coefficient of 'i' (√15) by -√3.
Simplifying the Expression
The final simplified form of the expression is -√5i.
Here's how we get there:
- We can rewrite the division as: (√15 * √-1) / (-√3)
- Simplifying the numerator: (√15 * i) / (-√3)
- Dividing the coefficients: √15 / -√3 = -√5
- Combining the result with 'i': -√5i
Key Takeaways
- Remember that the square root of a negative number involves imaginary numbers.
- Break down complex expressions into manageable steps.
- Simplify expressions using the properties of square roots and imaginary numbers.
Conclusion
The expression "Negative 15 Square Root divided by Negative Square Root 3" simplifies to -√5i. Understanding the concepts of imaginary numbers and the properties of square roots is crucial for navigating such calculations. By breaking down the problem into steps and applying the appropriate rules, we can arrive at the correct solution.