Question 41260
sqrt10+sqrt50
sqrt 50= sqrt10.sqrt5
so,

sqrt10+sqrt50 = sqrt10+sqrt10.sqrt5 

since sqrt10 is the common factor, we can write;

sqrt10+sqrt50 = sqrt10+sqrt10.sqrt5 = sqrt10(1+sqrt5)
So , the first answer you sent is right.

Let's talk about the second answer;

sqrt50 = sqrt 25.2= sqrt25.sqrt2 = 5.sqrt2 (Here we used that sqrt25 equals to 5)
So,

sqrt10+sqrt50 = sqrt10+5.sqrt2 

Therefore, your second answer is right, too.

When it comes to the last answer you sent;

sqrt10+sqrt50 = sqrt2.5 + sqrt 25.2= sqrt2.sqrt5+sqrt25.sqrt2 =

sqrt2.sqrt5 + 5.sqrt2 = sqrt2(sqrt5+5) (For the last step we factored out the common factor which was sqrt2.)

So, your last answer is also right.

I think first answer and last answer are in th simplest forms. However answer 2 can be simplified more. Actually answer 3 is the simplified form of answer 2.