Home » Simplify (frac{2sqrt{2} – sqrt{3}}{sqrt{2} + sqrt{3}})

Simplify (frac{2sqrt{2} – sqrt{3}}{sqrt{2} + sqrt{3}})

Simplify (frac{2sqrt{2} – sqrt{3}}{sqrt{2} + sqrt{3}})

  • A.
    3(sqrt{6} – 7)
  • B.
    3(sqrt{6} + 7)
  • C.
    3(sqrt{6} – 1)
  • D.
    3(sqrt{6} + 1)
Correct Answer: Option A
Explanation

(= frac{2sqrt{2} – sqrt{3}}{sqrt{2} + sqrt{3}} times frac{sqrt{2} – sqrt{3}}{sqrt{2} – sqrt{3}})
(= frac{2sqrt{2}(sqrt{2}) + (2sqrt{2})(-sqrt{3})-sqrt{3}(sqrt{2})-sqrt{3}(-sqrt{3})}{(sqrt{2})^2-(sqrt{3})^2})
(= frac{2 times 2 – 2sqrt{6} – sqrt{6} + 3}{2 – 3})
(= frac{4 – 3sqrt{6} + 3}{-1})
(= frac{7 – 3sqrt{6}}{-1})
(= frac{7}{-1} – frac{3sqrt{6}}{-1})
(= -7 + 3sqrt{6})
(= 3sqrt{6}-7)

There is an explanation video available below.

Explanation Video

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