Question 685346
How can you write this expression with a rationalized denominator? Please explain

Squareroot 3 - square root 6 / square root 3 + square root 6


{{{(sqrt(3) - sqrt(6))/(sqrt(3) + sqrt(6))}}}


{{{(sqrt(3) - sqrt(6))/(sqrt(3) + sqrt(6))}}} * {{{(sqrt(3) - sqrt(6))/(sqrt(3) - sqrt(6))}}} ---- Multiplying numerator and denominator by {{{sqrt(3) - sqrt(6)}}} in order to RATIONALIZE denominator


{{{((sqrt(3)*sqrt(3)) - (sqrt(6)sqrt(3)) - (sqrt(6)*sqrt(3)) - sqrt(6)* (-sqrt(6)))/((sqrt(3)*sqrt(3)) - (sqrt(6)sqrt(3)) + (sqrt(6)*sqrt(3)) + sqrt(6)* (-sqrt(6)))}}}


{{{(sqrt(9) - sqrt(18) - sqrt(18) + sqrt(36))/((sqrt(9) - sqrt(18) + sqrt(18) - sqrt(36)))}}}


{{{(3 - 2sqrt(18) + 6)/(3 - 6)}}} ---- {{{(9 - 2sqrt(18))/- 3}}} ----- {{{(9 - 2sqrt(9 * 2))/- 3}}} ----- {{{(9 - 2sqrt(3^2 * 2))/- 3}}} ----- {{{(9 - 6sqrt(2))/- 3}}} ----- {{{(3(3 - 2sqrt(2)))/- 3}}} ----- {{{(cross(3)(3 - 2sqrt(2)))/- 1cross(- 3)}}}


{{{- (3 - 2sqrt(2))}}}, or {{{highlight_green(- 3 + 2sqrt(2))}}}


You can do the check!!


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