Question 41260: Radical expressions
Three students were asked to simplify sqrt10 +sqrt50. Their answers were:
Sqrt10(1+sqrt5),
Sqrt10+5sqrt2, and
Sqrt2(5+sqrt5).
Which if any is correct?
Which is in simplest form?
Thanks so much
Found 2 solutions by Nate, zeynep:
Answer by Nate(3500)   (Show Source):
Answer by zeynep(43) (Show Source):
You can put this solution on YOUR website! 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.
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