What is the extraneous solution to the equation square root of 2 p plus 1 end root plus 2 square root of p is equal to 1 ?

Isolate the radical: √(2p + 1) = 1 − 2√p, then square both sides. This gives 2p + 1 = 1 − 4√p + 4p, so p = 0 or p = 4. Checking the original equation, p = 4 gives √9 + 2√4 = 3 + 4 = 7, not 1; therefore p = 4 is the extraneous solution, choice A.

AI-written and checked against the verified answer.