SOLUTION: I am not sure which answer is right Expres in simplest radical form sqrt 2 + sqrt 2/49 I have 2 answers 1.41 sqrt 1.41 over 7 or is it or is it 2/7 Thanks for any help

Algebra ->  Square-cubic-other-roots -> SOLUTION: I am not sure which answer is right Expres in simplest radical form sqrt 2 + sqrt 2/49 I have 2 answers 1.41 sqrt 1.41 over 7 or is it or is it 2/7 Thanks for any help      Log On


   

Question 202374This question is from textbook Algebra Structure and Method
: I am not sure which answer is right Expres in simplest radical form
sqrt 2 + sqrt 2/49 I have 2 answers 1.41 sqrt 1.41 over 7 or is it or is it 2/7
Thanks for any help This question is from textbook Algebra Structure and Method

Found 2 solutions by Theo, RAY100:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
I think what you are asking is:
Simplify sqrt%282%29+%2B+sqrt%282%2F49%29
If so, then the following applies:
since sqrt%282%2F49%29+=+sqrt%282%29%2Fsqrt%2849%29+=+sqrt%282%29%2F7+
then your equation becomes:
sqrt%282%29+%2B+%28sqrt%282%29%2F7%29
This should then be able to be simplified further as follows:
since sqrt%282%29 is the same as 7%2Asqrt%282%29%2F7
then your equation becomes:
sqrt%282%29+%2B+%28sqrt%282%29%2F7%29 = %287+%2A+sqrt%282%29+%2B+sqrt%282%29%29%2F7+ which can be simpified further to:
%288%2Asqrt%282%29%29%2F7
-----
what this says is that:
%288%2Asqrt%282%29%29%2F7 is the same as sqrt%282%29+%2B+sqrt%282%2F49%29 which you can prove to be true by using a calculator as I did.
what I got was
1.616244071 = 1.616244071 which was true so the reduction to the simplest form looks good.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt2 + sqrt(2/49)
,
sqrt2 + sqrt(2) /sqrt(49)
.
1*sqrt2 + (1/7)*sqrt2
.
1 1/7 *sqrt2,,,,,,,answer
.
or (8sqrt2)/7
.
.
numerically this is 1.616,,,as is the original