Answer:
[tex]5i\sqrt{7}[/tex]
Step-by-step explanation:
In order to solve this question we need to know how to multiply roots. You will need to understand that when we multiply [tex]\sqrt{a}[/tex] by [tex]\sqrt{b}[/tex], the following is true.
[tex](\sqrt{a})(\sqrt{b}) = \sqrt{ab}[/tex] (1)
From the question it self we know that [tex]\sqrt{ab}[/tex] is equal to [tex]\sqrt{-175}[/tex]. We also know that [tex]i^{2} = -1[/tex] or in other words [tex]i = \sqrt{-1}[/tex].
Now we will need to factors [tex]\sqrt{-175}[/tex] so that at the end we will end up representing [tex]\sqrt{-175}[/tex] as a product of [tex]\sqrt{-1}[/tex] and some other number. In order to determine the unknown number we will just have to divide [tex]\sqrt{-175}[/tex] by [tex]\sqrt{-1}[/tex]. From the equation (1) that I mention at the start we can figure out that......
[tex]\sqrt{a} = \frac{\sqrt{-175} }{\sqrt{-1} } = \sqrt{175}[/tex] (in our case [tex]\sqrt{a}[/tex] is the unknown number we are trying to find)
Now we can rewrite [tex]\sqrt{-175}[/tex] as the following.....
[tex]\sqrt{-175} = (\sqrt{175})(\sqrt{-1})[/tex]
From here we substitute [tex]\sqrt{-1}[/tex] with [tex]i[/tex] and simplify [tex]\sqrt{175}[/tex]. In order to simplify [tex]\sqrt{175}[/tex] we will have to factor [tex]\sqrt{175}[/tex] in a way that we will see [tex]\sqrt{175}[/tex] as a multiple of a perfect square root. An so we get the following
[tex]\sqrt{-175} = (\sqrt{175})(i) = (\sqrt{7})(\sqrt{25} )(i) = (\sqrt{7})(5)(i) = 5i\sqrt{7}[/tex]
