Rewrite the following irrational numbers in ascending order of magnitude.
`(i)3sqrt(18),6sqrt(144),sqrt(7)" "(ii)3sqrt(12),sqrt(20),6sqrt(25),sqrt(6),12sqrt(112)`

Explanation

(i) The given surds are of order 3,6 and 2 respectively. L.C.M. of 3,6 and 2 is 6. So, we convert each surd into a surd of order 6.

Since, `144lt324lt353`
`rArr""6sqrt(144)lt6sqrt(324)lt6sqrt(343)rArr6sqrt(144)lt6sqrt(18)lt6sqrt(7)`
(ii) The given surds are of orders 3,4,6,2,12 whose L.C.M. is 12.

Since, `112lt625lt8000lt20736lt46656`
i.e.,`12sqrt(112)lt12sqrt(625)lt12sqrt(80000)lt12sqrt(20736)lt12sqrt(46656)`
i.e.,`12sqrt(112),6sqrt(25),4sqrt(20),3sqrt(12),sqrt(6)` in ascending order.