Question

I have tried solving this problem over and over but I'm still not sure with my answer.
The question is sqrt2 / 2 + sqrt2.
I think the answer is 1/sqrt2 + sqrt2 because you have to cancel out the common factors.

Answer 1

Don't know what you want done with "solve"
We solve equations, but you don't have one.
Did you mean "evaluate" ?

Also , did you mean it the way you typed it, or did you mean
√2/(2+√2) ?

Back before we had calculators, it was often useful to have this rationalized, if so , then ...

= √2/(2+√2) * (2 - √2)/(2 - √2)
= (2√2 - 2)/(4-2)
= 2( √2 - 1)/2

= √2 - 1

you can usually check this kind of work by evaluating the original and the final answer on your calculator.
My answer is correct

Answer 2

Yes, sorry I meant evaluate. But the equation is not √2/(2+√2). The equation is √2/2 + √2

Answer 3

ok, that makes it easy

√2/2 + √2
= √2( 1/2 + 1)
= √2(3/2)
= 3√2/2