[email protected] wrote:What is the solution of [√(7 + √48) + √(7 - √48)]² ?
(A) 1
(B) 7 - 4√3
(C) 14 - 4√3
(D) 14
(E) 16
We can reason our way to the correct answer.
√x + √y > √(x+y)
To illustrate:
√4 + √9 > √(4+9)
5 > √13.
Looking at the given expression, we can quickly deduce that it must be greater than 14:
√(7 + √48) + √(7 - √48) > √(7 + √48 + 7 - √48)
√(7 + √48) + √(7 - √48) > √14
Squaring both sides:
[√(7 + √48) + √(7 - √48)]² > (√14)²
[√(7 + √48) + √(7 - √48)]² > 14
Only one answer choice is greater than 14.
The correct answer is
E.
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