The expression resembles this form: (a - b)^2 where a = (7 + (29)^0.5)^0.5 b = (7 - (29)^0.5)^0.5 (a - b)^2 a^2 + b^2 - 2ab a^2 = 7 + (29)^0.5 b^2 = 7 - (29)^0.5 2ab = 2*[(7 + (29)^0.5)(7 - (29)^0.5)]^0.5 = 2*[20]^0.5 = 4*[5]^0.5 So (a - b)^2 = 7 + 7 - 4[5]^0.5 = 14 - 4[5]^0.5 [spoiler](C)[/spoiler] is the answer

aneesh.kg wrote:The expression resembles this form: (a - b)^2 where a = (7 + (29)^0.5) b = (7 - (29)^0.5) (a - b)^2 a^2 + b^2 - 2ab a^2 = 7 + (29)^0.5 b^2 = 7 - (29)^0.5 2ab = 2*(7 + (29)^0.5)(7 - (29)^0.5) = 2*(49 - 29) = 40 So (a - b)^2 = 7 + 7 - 40 = - 26 [spoiler](A)[/spoiler] is the answer Wrong! You missed the whole root!!!

Ah, Yes I did. Thanks. Corrected the post above. Corrected Solution: The expression resembles this form: (a - b)^2 where a = (7 + (29)^0.5)^0.5 b = (7 - (29)^0.5)^0.5 (a - b)^2 a^2 + b^2 - 2ab a^2 = 7 + (29)^0.5 b^2 = 7 - (29)^0.5 2ab = 2*[(7 + (29)^0.5)(7 - (29)^0.5)]^0.5 = 2*[20]^0.5 = 4*[5]^0.5 So (a - b)^2 = 7 + 7 - 4[5]^0.5 = 14 - 4[5]^0.5 [spoiler](C)[/spoiler] is the answer

What is the value of [√(7+√29) - √(7-√29)]²? -26 2√29 14-4√5 14 14+4√5 The square of a value must be nonnegative. Eliminate A. Ballpark. [√(7+√29) - √(7-√29)]² ≈ [√(7+6) - √(7-6)]² Since √25=5 and √36=6, √29 is between 5 and 6. ≈ (√13 - 1)² ≈ 3² Since √9=3 and √16=4, √13 is between 3 and 4. ≈ 9. Since we overestimated the value of √13-1, the correct answer must be less than 9. Only answer choice C works: 14-4√5 ≈ 14-8 ≈ 6. The correct answer is C. If we couldn't ballpark because the answer choices were closer in value, we could use the following approach. Remembering that (a-b)² = a²-2ab+b², use substitution: Let x=7 and y=√29. Substituting x=7 and y=√29 into [√(7+√29) - √(7-√29)]², we get: (√(x+y) - √(x-y))² = (x+y) - 2√((x+y)(x-y)) + (x-y) = 2x - 2√(x²-y²) = 2*7 - 2√(7² - 29) = 14 - 2√20 = 14 - 4√5. The correct answer is C.