Perform the indicated operations and write the result in standard form
3 sq root -16 + 2 sq root -81
Is 3 sqrt -16 supposed to mean (sqrt 3) -16 or 3*(sqrt -16) ??
If you are talking about the square root of negative numbers, the answer will be a complex number. Are you studying complex numbers?
yes I am
yes am
To perform the indicated operations, we need to simplify each square root separately and then combine the results.
Let's start with the first term: √(-16).
We know that the square root of a negative number doesn't yield a real number, but we can use the concept of imaginary numbers. The square root of -1 is denoted by "i". Therefore, we can rewrite the square root of -16 as follows:
√(-16) = √(16 * -1) = √16 * √-1 = 4i
The second term is: √(-81).
Again, we can rewrite this by separating the factors:
√(-81) = √(-1 * 81) = √81 * √-1 = 9i
Now, we can combine the simplified terms and perform the addition:
3√(-16) + 2√(-81) = 3(4i) + 2(9i)
Multiplying the coefficients by the imaginary unit "i":
= 12i + 18i
Combining like terms:
= (12 + 18)i
= 30i
Therefore, the result in standard form is 30i.