Question
Download Solution PDFIf the positive square root of (5 + 3√2) (5 - 3√2) is α, then what is the positive square root of 8 + 2α ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
(a - b) (a + b) = a2 - b2
(a2 + 2ab + b2) = (a + b)2
Calculation:
Given that,
α = √[(5 + 3√2) (5 - 3√2)]
Since, (a - b) (a + b) = a2 - b2
α = √[(52 - (3√2)2]
α = √(25 - 18) = √7
Let the required square root is β
β = √(8 + 2√7) = √(7 + 1 + 2√7)
β = √[(√7)2 + 2.1.√7 + (1)2]
β = √(√7 + 1)2
Since, (a2 + 2ab + b2) = (a + b)2
β = √7 + 1
Last updated on May 29, 2025
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