SOLUTION: Simplify: {{{sqrt( (sqrt(21)-2sqrt(7))^2)}}}

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify: {{{sqrt( (sqrt(21)-2sqrt(7))^2)}}}      Log On


   

Question 1060419: Simplify:
sqrt%28+%28sqrt%2821%29-2sqrt%287%29%29%5E2%29
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The inside is a trinomial but of known numbers.
sqrt%2821%29sqrt%2821%29-2%2A2%2Asqrt%2821%29sqrt%287%29%2B4%2Asqrt%287%29sqrt%287%29
21-4sqrt%283%2A7%2A7%29%2B4%2A7
21%2B28-4%2A7%2Asqrt%283%29
49-28%2Asqrt%283%29

All that is inside the square root function.
sqrt%2849-28%2Asqrt%283%29%29

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Simplify:
sqrt%28+%28sqrt%2821%29-2sqrt%287%29%29%5E2%29
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

sqrt%28+%28sqrt%2821%29-2sqrt%287%29%29%5E2%29  has TWO values.


One value is  sqrt%2821%29-2sqrt%287%29.


Another value is  -%28sqrt%2821%29-2sqrt%287%29%29 = 2sqrt%287%29+-+sqrt%2821%29.


Same  as  sqrt%28a%5E2%29  has two values.  One is  |a|.  Another is  -|a|.
For any real a =/= 0.


If a = 0, then  sqrt%280%29 = 0  has only one value.

Calculations that "josgarithmetic" does in his response, are absolutely unnecessary.
They do not lead to the simplest form.
In opposite, they require to be simplified further.

So, writing by "josgaritmetic" is totally out of the goal of this assignment.