Question

How do I simplify the following radical expression?

Answer 1

\[\frac{ \sqrt{50} }{5 } + \frac{ \sqrt{2} }{ 10}\]

Answer 2

Well, there's a few things we can do. We can use a common denominator and make it into one fraction first. But me personally, I don't think that is best. So quick question. 5 is the square root of what number?

Answer 3

25

Answer 4

Correct. So this is what we can do. Make sure it makes sense:
\[\frac{ \sqrt{50} }{ 5 }=\frac{ \sqrt{50} }{ \sqrt{25} } \]

Answer 5

right because 5 is the root of 25

Answer 6

Yep. Now here's the next part:
\[\frac{ \sqrt{50} }{ \sqrt{25} }=\sqrt{\frac{ 50 }{ 25 }}=\sqrt{2} \]Kinda see what I did?

Answer 7

Yeah, I see

Answer 8

Yep. Now I would finally make what we have into one fraction.
\[\sqrt{2}+\frac{ \sqrt{2} }{ 10 }\]Do you know how to find a commond enominator and make that into one fraction?

Answer 9

Yeah, would it be:\[\frac{ 10\sqrt{2} }{ 10 } + \frac{ \sqrt{2} }{ 10}\]

Answer 10

Right. So now we would have:
\[\frac{ 10\sqrt{2}+\sqrt{2} }{ 10 }=\frac{ 11\sqrt{2} }{ 10 }\]And I would say that is as simplified as you can get :3

Answer 11

Thank you!! :)

Answer 12

Sure ^_^