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evaluate sqrt(5+2*(sqrt6)) + sqrt(8-2*(sqrt15))

  • maths - ,

    Use: √(a+2√(ab)+b) = √a + √b
    Too: √(a-2√(ab)+b) = √a - √b

    √(5+2√6) + √(8-2√15)
    = √(2+2√2√3+3) + √(8-2√15)
    = √((√2+√3)^2) + √(8-2√15)
    = √2 + √3 + √(8-2√15)
    = √2 + √3 + √(5-2√3√5+3)
    = √2 + √3 + √((√5-√3)^2)
    = √2 + √3 + √5 - √3
    = √2 + √5

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