Preliminary SAT (PSAT) Practice Test

To determine the value of √-9 expressed in terms of i, we start by recognizing that the square root of a negative number involves the imaginary unit i, where i is defined as √-1.

First, we can break down √-9 using the property of square roots that states √(a * b) = √a * √b. Here, -9 can be rewritten as -1 times 9:

√-9 = √(-1 * 9) = √-1 * √9.

Since we know that √-1 is equal to i, we substitute that in:

√-9 = i * √9.

Next, we find √9. The square root of 9 is simply 3 because 3 multiplied by itself gives 9:

√9 = 3.

Now, substituting back, we get:

√-9 = i * 3 = 3i.

Thus, the expression for √-9 in terms of i is 3i, confirming that this is the correct answer.