Final answer:
The given radical expression 2 / (√32 - 5√2) was simplified using rationalization. After simplification, the result did not match any of the given options, so 'None of the above' is the correct choice.
Step-by-step explanation:
The student asked which of the following radical expressions is equivalent to 2 / (√32 - 5√2).
To solve such an expression, we should rationalize the denominator.
This involves multiplying the numerator and the denominator by the conjugate of the denominator which is (√32 + 5√2).
Let's first simplify √32.
Since 32 = 16 * 2 and the square root of 16 is 4, √32 = 4√2. Our expression now looks like 2 / (4√2 - 5√2).
Combining like terms in the denominator, we get 2 / (-√2).
Multiplying both numerator and denominator by the conjugate of the denominator, we get:
(2 * (√2 + 5√2)) / ((-1)(2 - 25))
Which simplifies to (2√2 + 10√2) / 23 or 2(√2 + 5) / 23.
Comparing this with the given options, none of them match exactly, so the correct answer is None of the above.