Completely simplify and rationalize the denominator:$$\frac{\sqrt{160}}{\sqrt{252}}\times\frac{\sqrt{245}}{\sqrt{108}}$$
+128408 sqrt (160) = sqrt (16 * 10) = sqrt (16) * sqrt (10) = 4sqrt (10)
sqrt (252) = sqrt ( 63 * 4) = sqrt ( 9 * 7 * 4) = sqrt (36 *7) = sqrt (36) * sqrt (7) = 6sqrt (7)
sqrt (245) = sqrt ( 49 * 5) = sqrt (49) * sqrt (5) = 7sqrt (5)
sqrt (108) = sqrt (36 * 3) = sqrt (36) * sqrt (3) = 6sqrt (3)
So we have
4sqrt (10) 7sqrt (5) 28sqrt (50) 7 sqrt (25) (sqrt (2)
_________ * _________ = __________ = __________________ =
6sqrt (7) 6sqrt (3) 36 sqrt (21) 9 sqrt (21)
7 * 5 sqrt (2) 35 sqrt (2) sqrt (21) 35 sqrt (42)
____________ = __________ ________ = ___________ =
9 sqrt (21) 9 sqrt (21) sqrt (21) 9 * 21
35 sqrt ( 42) 5 sqrt (42) 5sqrt (42)
___________ = __________ = __________
21 * 9 3 * 9 27
