Home » Simplify (frac{5}{sqrt{3}}-frac{3}{sqrt{2}})

Simplify (frac{5}{sqrt{3}}-frac{3}{sqrt{2}})

Simplify (frac{5}{sqrt{3}}-frac{3}{sqrt{2}})
  • A.
    (frac{1}{6}(5sqrt{3}-3sqrt{2})
  • B.
    (frac{1}{6}(15sqrt{3}-6sqrt{2})
  • C.
    (frac{1}{6}(3sqrt{2}-sqrt{3})
  • D.
    (frac{1}{6}(10sqrt{3}-9sqrt{2})
Correct Answer: Option D
Explanation

(frac{5}{sqrt{3}}-frac{3}{sqrt{2}}=frac{5sqrt{2}-3sqrt{3}}{sqrt{6}}\
=frac{5sqrt{2}-3sqrt{3}}{sqrt{6}} times frac{sqrt{6}}{sqrt{6}}Rationalize\
frac{sqrt{6}(5sqrt{2}-3sqrt{3})}{6}\
frac{5sqrt{12}-3sqrt{18}}{6}=frac{10sqrt{3}-9sqrt{2}}{6}\
frac{1}{6}(10sqrt{3}-9sqrt{2}))