There are different methods which can be used:
First option: Combine the radicals:
(sqrt9sqrt8)/(sqrt6sqrt6) = sqrt72/sqrt36 = sqrt(72/36) = sqrt2
Second option: Simplify where possible, find factors of radicands.
(color(red)(sqrt9)color(blue)(sqrt8))/(color(green)(sqrt6sqrt6))
=(color(red)(3)color(blue)(sqrt(4xx2)))/(color(green)(sqrt6)^2)
=(color(red)(3)color(blue)(xx2sqrt(2)))/(color(green)(6)
=sqrt2
Third option: Write as the product of prime factors:
(sqrt9sqrt8)/(sqrt6sqrt6)
=(sqrt3 xx sqrt3 xxsqrt2xx sqrt2xx sqrt2)/(sqrt2xxsqrt3xxsqrt2xx sqrt3)" " now cancel
=(cancelsqrt3 xx cancelsqrt3 xxcancelsqrt2xx cancelsqrt2xx sqrt2)/(cancelsqrt2xxcancelsqrt3xxcancelsqrt2xx cancelsqrt3)
=sqrt2