SOLUTION: Express {{{ 2+4sqrt6/3sqrt2-3 }}} in the form {{{p sqrt2+q sqrt3 }}} where p and q are rational numbers.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Express {{{ 2+4sqrt6/3sqrt2-3 }}} in the form {{{p sqrt2+q sqrt3 }}} where p and q are rational numbers.      Log On


   

Question 984832: Express +2%2B4sqrt6%2F3sqrt2-3+ in the form p+sqrt2%2Bq+sqrt3+ where p and q are rational numbers.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
+2%2B4sqrt6%2F3sqrt2-3+

Say this better as 2+4*sqrt(6)/(3*sqrt(2))-3
rendered as 2%2B4%2Asqrt%286%29%2F%283%2Asqrt%282%29%29-3.

2%2B%284%2Asqrt%282%29sqrt%283%29%29%2F%283%2Asqrt%282%29%29-3

2%2B%284%2Across%28sqrt%282%29%29sqrt%283%29%29%2F%283%2Across%28sqrt%282%29%29%29-3

2-3%2B%284%2Asqrt%283%29%29%2F%283%29

-1%2B%284%2F3%29sqrt%283%29, and not much more that can be done with the rational integer, -1; you could put it as this for final requested form of the result:

highlight%28-1%2Asqrt%281%29%2B%284%2F3%29sqrt%283%29%29