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Ruel The Midianite
Lv 4
Ruel The Midianite asked in Science & MathematicsMathematics · 2 years ago

Simplify sqrt(4 + 2 sqrt(3)) - sqrt(3)?

3 Answers

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  • ?
    Lv 7
    2 years ago
    Favorite Answer

    Let sqr(x)+sqr(y)=sqr[4+2sqr(3)], then

    [sqr(x)+sqr(y)]^2=4+2sqr(3)

    =>

    x+y+2sqr(xy)=4+2sqr(3)

    =>

    x+y=4

    xy=3

    =>

    x=3

    y=1

    thus,

    sq[4+2sqr(3)]-sqr(3)

    =

    sqr(3)+sqr(1)-sqr(3)

    =

    1

  • ?
    Lv 7
    2 years ago

    sqrt(4 + 2 sqrt(3)) - sqrt(3)

    = 1

    Source(s): https://www.wolframalpha.com/input/?i=sqrt(4+%2B+2...
  • kb
    Lv 7
    2 years ago

    Note that 4 + 2√3 = (1 + 3) + 2√3 = 1 + 2√3 + (√3)² = (1 + √3)².

    So, √(4 + 2√3) = 1 + √3 [noting that 1 + √3 > 0].

    Therefore, √(4 + 2√3) - √3 = (1 + √3) - √3 = 1.

    I hope this helps!

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