Perform the indicated operations and write the result in standard form

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.