Completely simplify and rationalize the denominator: $$\frac{\sqrt{160}}{\sqrt{252}}\times\frac{\sqrt{245}}{\sqrt{180}}$$
+128406 sqrt (160) = sqrt (16 *10) = 4sqrt 10
sqrt (252) = sqrt (36 * 7) = 6sqrt 7
sqrt (245) = sqrt ( 49 * 5) = 7sqrt 5
sqrt (180) = sqrt (36 * 5) = 6 sqrt (5)
So we have
4sqrt (10) 7 sqrt (5) 28sqrt (10)
_________ * __________ = ____________ =
6 sqrt (7) 6 sqrt (5) 36 sqrt (7)
(7/9) sqrt ( 10) / sqrt (7) =
(7/9) sqrt (70) / 7 =
sqrt ( 70) * 7/63 =
sqrt (70) / 9
