SOLUTION: What sort of approach should i do, when im faced with a question such as: Given that {{{ (a-sqrt(b))^2=(a^2+b)-2a*sqrt(b) }}}, then {{{ sqrt(28+10sqrt(3)) }}} is equal to: A)

Algebra ->  Radicals -> SOLUTION: What sort of approach should i do, when im faced with a question such as: Given that {{{ (a-sqrt(b))^2=(a^2+b)-2a*sqrt(b) }}}, then {{{ sqrt(28+10sqrt(3)) }}} is equal to: A)      Log On


   

Question 1021600: What sort of approach should i do, when im faced with a question such as:
Given that +%28a-sqrt%28b%29%29%5E2=%28a%5E2%2Bb%29-2a%2Asqrt%28b%29+, then +sqrt%2828%2B10sqrt%283%29%29+ is equal to:
A) +abs%28-5-sqrt%283%29%29+
B) +5-sqrt%283%29+
C) +abs%28sqrt%283%29-5%29+
D) +3%2Bsqrt%285%29+
E) +3-sqrt%285%29+
What is the answer between these multiple choices, and how may i get to that answer?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
You would be better off if you considered +%28a%2Bsqrt%28b%29%29%5E2=%28a%5E2%2Bb%29%2B2a%2Asqrt%28b%29+.
==> +%28a%2Bsqrt%28b%29%29%5E2=%28a%5E2%2Bb%29%2B2a%2Asqrt%28b%29+=+28%2B10sqrt%283%29+.
This implies
2a = 10 and a%5E2%2Bb+=+28
==> a = 5 and 5%5E2%2Bb+=+25%2Bb+=+28 ==> b = 3
Therefore,
+%285%2Bsqrt%283%29%29%5E2+=+28%2B10sqrt%283%29+.
Taking square roots of both sides of the last equation, we get
abs%285%2Bsqrt%283%29%29+=+sqrt%2828%2B10sqrt%283%29%29.
But abs%285%2Bsqrt%283%29%29+=+abs%28-5-sqrt%283%29%29, so now you know the answer!