How do you evaluate #\frac { 10} { 3\sqrt { 6} - 7\sqrt { 2} }#?

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Answer 1 · 2017-07-07T22:12:57

See a solution process below:

First, we will rationalize the denominator (remove all radicals from the denominator) by multiplying the fraction by the appropriate form of #1#:

#(3sqrt(6) + 7sqrt(2))/(3sqrt(6) + 7sqrt(2)) xx 10/(3sqrt(6) - 7sqrt(2)) =>#

#(10(3sqrt(6) + 7sqrt(2)))/(3^2(sqrt(6))^2 - 21sqrt(6)sqrt(7) + 21sqrt(6)sqrt(7) - 7^2(sqrt(2))^2) =>#

#((10 xx 3sqrt(6)) + (10 xx 7sqrt(2)))/((9 * 6) - 0 - (49 * 2)) =>#

#(30sqrt(6) + 70sqrt(2))/(54 - 98) =>#

#(30sqrt(6) + 70sqrt(2))/-44#

If necessary to get to a single number:

#sqrt(6) = 2.449# rounded to the nearest thousandth

#sqrt(2) = 1.414# rounded to the nearest thousandth

Substituting gives:

#((30 * 2.449) + (70 * 1.414))/-44 =>#

#(73.47 + 98.98))/-44 =>#

#172.45/-44 =>#

#-3.919#