Help Please?
1.30√-25 x 8√-49
2. 6√-64 + 12√-36
3. 4√-13 - 6√-13
30√-25 x 8√-49
= 30√25√-1 x 8√49√-1
=150√-1 x 56√-1
= 8400 (-1)
= -8400 , remember that √-1 x √-1 = i x i = i^2 = -1
do the others the same way, let me know what you got
I'm Doing Problem 2 Right Now .
But I'm Stuck How Did You Get 150 In the 3rd Line?
30√25√-1 x 8√49√-1
= 30 x 5 x √-1 x 8 x 7 x √-1
= 150 x √-1 x 56 x √-1
= 8400 x i^2
= ....
Oh Okay .
I Tried The Other Two Problems.
For #1 I Got 120 As My Answer.
For #2 I Got 37 As My Answer.
Nope:
6√-64 + 12√-36 = 6*8i + 12*6i = 120i
4√-13 - 6√-13 = (4-6)√-13 = -2√13 i
Sure! Let's solve each of these problems step-by-step:
1. We have the expression 1.30√-25 x 8√-49. To simplify this expression, we can start by simplifying each square root individually.
- The square root of -25 can be written as √(-1 * 25). We can take out the square root of -1 as "i" (the imaginary unit): i√25.
- Similarly, the square root of -49 can be written as √(-1 * 49), which simplifies to i√49.
Now, substituting these simplified square roots back into the original expression:
1.30 * i√25 * 8 * i√49
Next, we can multiply the numbers outside the square roots:
1.30 * 8 * i√25 * i√49
Following the order of operations, we multiply the numbers first:
10.4 * i√25 * i√49
Next, we simplify the square roots within the expression:
10.4 * i * 5 * i * 7
Since i * i is equal to -1, we can further simplify the expression:
10.4 * (-1) * 5 * 7
Finally, calculate the product:
-364
Therefore, the solution to 1.30√-25 x 8√-49 is -364.
2. We have the expression 6√-64 + 12√-36. Let's follow the same step-by-step process as before:
- The square root of -64 can be written as √(-1 * 64), which simplifies to i√64.
- The square root of -36 can be written as √(-1 * 36), which simplifies to i√36.
Now, substituting these simplified square roots back into the original expression:
6 * i√64 + 12 * i√36
Next, we can multiply the numbers outside the square roots:
6 * i√64 + 12 * i√36
Following the order of operations, we multiply the numbers first:
6i * 8 + 12i * 6
Now, we simplify the expression:
48i + 72i
Adding like terms, we get:
120i
Therefore, the solution to 6√-64 + 12√-36 is 120i.
3. We have the expression 4√-13 - 6√-13. Again, let's follow the same step-by-step process:
- The square root of -13 can be written as √(-1 * 13), which simplifies to i√13.
Now, substituting this simplified square root back into the original expression:
4 * i√13 - 6 * i√13
Next, we can multiply the numbers outside the square roots:
4i * √13 - 6i * √13
Simplifying the expression:
(4i - 6i) * √13
Combining like terms, we get:
-2i * √13
Therefore, the solution to 4√-13 - 6√-13 is -2i√13.
I hope this explanation helps you understand how to solve these types of problems! If you have any further questions, feel free to ask.