Which of the following is equivalent to Start Root negative 50 End Root?
(1 point)
Responses
5 Start Root 2 End Root
Image with alt text: 5 Start Root 2 End Root
5 i Start Root 2 End Root
Image with alt text: 5 i Start Root 2 End Root
5 Start Root 2 i End Root
Image with alt text: 5 Start Root 2 i End Root
negative 5 Start Root 2 End Root
Image with alt text: negative 5 Start Root 2 End Root
To determine which of the following is equivalent to Start Root negative 50 End Root, we need to simplify the square root of negative 50.
The square root of a negative number is not a real number, but it can be represented using the imaginary unit i. The imaginary unit i is defined as the square root of -1.
To simplify the square root of negative 50, we can factor out the largest perfect square from within the radicand (the expression inside the square root). In this case, the largest perfect square that can be factored out is 25, which is the square of 5.
So, we have:
Start Root negative 50 End Root = Start Root negative 1 times 25 times 2 End Root = Start Root negative 1 times 25 End Root times Start Root 2 End Root
The square root of 25 is 5, and the square root of 2 is an irrational number, so we represent it as Start Root 2 End Root.
Combining the simplified values, we get:
Start Root negative 50 End Root = 5 Start Root 2 End Root
Therefore, the equivalent expression is 5 Start Root 2 End Root.