Simplify sqrt(-8)times sqrt(-12)
To simplify the expression sqrt(-8) times sqrt(-12), we can start by simplifying each square root individually.
The square root of -8 can be simplified as follows:
1. We know that the square root of a negative number is not a real number, so we need to rewrite -8 in terms of the imaginary unit "i" (which is defined as sqrt(-1)). This can be done by factoring out -1 from -8:
-8 = -1 * 8
2. Now, we can rewrite the square root of -8 as the square root of -1 times the square root of 8:
sqrt(-8) = sqrt(-1 * 8)
3. Using the property of square roots, we can split the expression and simplify separately:
sqrt(-8) = sqrt(-1) * sqrt(8)
4. The square root of -1 is equal to "i":
sqrt(-8) = i * sqrt(8)
Similarly, let's simplify the square root of -12:
1. We need to rewrite -12 in terms of "i":
-12 = -1 * 12
2. Rewrite the square root of -12 as the square root of -1 times the square root of 12:
sqrt(-12) = sqrt(-1 * 12)
3. Use the property of square roots to split the expression and simplify:
sqrt(-12) = sqrt(-1) * sqrt(12)
4. The square root of -1 is equal to "i":
sqrt(-12) = i * sqrt(12)
Now that we have simplified each square root term, we can combine them by multiplying:
sqrt(-8) * sqrt(-12) = (i * sqrt(8)) * (i * sqrt(12))
When we multiply "i" with "i", we get "i²" which is equal to -1:
sqrt(-8) * sqrt(-12) = -1 * sqrt(8) * sqrt(12)
Finally, we can combine the square roots and simplify further if possible.