Mathematics

Simplify (frac{1}{sqrt{3}+2}) in the form (a+bsqrt{3})

Simplify (frac{1}{sqrt{3}+2}) in the form (a+bsqrt{3})
  • A.
    2 -√3
  • B.
    -2 – √3
  • C.
    2 + √3
  • D.
    -2 + √3
Correct Answer: Option A
Explanation

(frac{1}{sqrt{3}+2}=frac{1}{sqrt{3}+2}times frac{sqrt{3}-2}{sqrt{3}-2}\=frac{sqrt{3}-2}{(sqrt{3})^{2} -2^{2}}\=frac{sqrt{3}-2}{3-4}=frac{sqrt{3}-2}{1}\=-sqrt{3}+2\=2-sqrt{3})