I'm doing some practice questions for my Complex Numbers unit and I'm confused on how to get the answer for this problem: (Radical -50x^2y^2) My answer guide says that the answer is 5i |xy| (Radical 2) Could someone please show me how to do the problem? Thanks
First, √x^2 is |x| since √ is always positive.
That is, √4 = 2, not ±2
Just because (-2)^2 is also 4 does not mean that -2 is √4
And, since √-50 = √50 √-1 = √25*√2*√-1= 5√2 i
the result is as given: 5i |xy| √2
sqrt(-50x^2y^2) = sqrt(25*2*(-1)x^2y^2) = 5i(xy)sqrt(2).
Note:
sqrt 25 = 5,
sqrt (-1) = i,
2 remains under radical.
Thanks for your help. I understand now and it helped me when solving the other problems in this unit. I appreciate it!!!
Sure! I can help you with that. To simplify the expression (Radical -50x^2y^2), we can break it down step by step.
Step 1: Start by factoring out any perfect squares from under the radical sign. In this case, -50 can be factored as -1 * 2 * 5^2.
(Radical -1 * 2 * 5^2 * x^2 * y^2)
Step 2: Split the radical sign into two separate radicals, one containing the perfect squares and the other containing the remaining terms.
(Radical -1) * (Radical 2) * (Radical 5^2) * (Radical x^2) * (Radical y^2)
Step 3: Simplify each radical separately.
(Radical -1) becomes "i" since the square root of -1 is represented as "i".
(Radical 5^2) becomes 5, as the square root of 5^2 is 5.
(Radical x^2) simplifies to x, as the square root of x^2 is x.
(Radical y^2) simplifies to y, as the square root of y^2 is y.
So, we have: i * (Radical 2) * 5 * x * y
Step 4: Rearrange the terms for better readability.
5 * i * |xy| * (Radical 2)
Note that |xy| is the absolute value of xy, which ensures that the value inside the absolute value brackets is positive.
Therefore, the simplified expression of (Radical -50x^2y^2) is 5i |xy| (Radical 2).
I hope this explanation helps! Let me know if you have any further questions.