Which statement is true about the difference 2 square root of 7 − square root of 26?

it is rational and equal to −2.
it is rational and equal to 0.
it is irrational and equal to −2 square root of 7.
it is irrational and equal to square root of 7.

“Sqrt” will represent square root. Apologies for the lack of TEX - I’m on mobile.

To find 2sqrt(7) in a different way, we can first take that 2 is the square root of 4, so we can have sqrt(4)sqrt(7)=sqrt(28). Thus, 2sqrt(7)-sqrt(26)>0. Next, given that, our only remaining possibility is then sqrt(7). However, in order for that to be true, we must factor values out such that (2)(sqrt(7))-(sqrt(7))=sqrt(7). However, sqrt(26) is not equal to sqrt(7), and we can therefore not factor that out to make the function equal to sqrt(7) and we therefore have no correct answer given.

Feel free to ask further questions, and good luck!