化简:√{[1-√(1-0.5^2)]^2+0.5^2}

红树

化简:√{[1-√(1-0.5^2)]^2+0.5^2}

luyuanhong

     √{[1-√(1-0.5^2)]^2+0.5^2}

= √[1-2√(1-0.5^2)+1-0.5^2+0.5^2]

= √[2-2√(1-0.5^2)]

= √[2-2√(1-1/4)]

= √[2-2√(3/4)]

= √(2-√3)

= √[(4-2√3)/2]

= √(3-2√3+1)/√2

= √(√3-1)^2/√2

= (√3-1)/√2

= (√6-√2)/2 。