BTGModeratorVI wrote: ↑Wed Mar 25, 2020 6:18 am
What is the value of 2/(2−√2)?
(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4\
Answer:
D
Source: Veritas Prep
When we have a radical or radical expression in the denominator, we must rationalize the denominator, in this case by multiplying the numerator and denominator by the conjugate of (2 - √2), which is (2 + √2).
2 / (2−√2) x (2+√2) / (2+√2)
Note that when the expressions in the denominator are FOILed, we obtain 4 + 2√2 - 2√2 - 2, which simplifies to 4 - 2.
2(2+√2) / (4 - 2)
2(2+√2) / 2
2 + √2
Answer: D
