GMAT Prep radical expression
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Take, √(9 + √80) = a and √(9 - √80) = b
Hence, we need to find the value of (a + b)² = a² + 2ab b²
a² = [√(9 + √80)]² = (9 + √80)
b² = [√(9 - √80)]² = (9 - √80)
ab = [√(9 - √80)]*[√(9 - √80)] = √[(9 - √80)(9 - √80)] = 9² - (√80)² = 81 - 80 = 1
Thus, a² + b²= (9 + √80) + (9 - √80) = 18
Hence, (a + b)² = a² + 2ab b² = 18 + 2 = 20
The correct answer is E.
Hence, we need to find the value of (a + b)² = a² + 2ab b²
a² = [√(9 + √80)]² = (9 + √80)
b² = [√(9 - √80)]² = (9 - √80)
ab = [√(9 - √80)]*[√(9 - √80)] = √[(9 - √80)(9 - √80)] = 9² - (√80)² = 81 - 80 = 1
Thus, a² + b²= (9 + √80) + (9 - √80) = 18
Hence, (a + b)² = a² + 2ab b² = 18 + 2 = 20
The correct answer is E.
Anurag Mairal, Ph.D., MBA
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