`a) sqrt{150.27.96}`
`=sqrt{2.3.5^2. 3^3. 2^5. 3}`
`=sqrt{2^6. 3^4. 5^2. 3}`
`=sqrt{(2^3. 3^2. 5)^2. 3}`
`=sqrt{360^2. 3}`
`=360sqrt{3}`
`b) sqrt{225/4. 81/25. 49/64}`
`=sqrt{(15/2)^2. (9/5)^2. (7/8)^2}`
`=sqrt{(15/2. 9/5. 7/8)^2}`
`=sqrt{(189/16)^2}`
`=189/16`
`c) sqrt{137^2-88^2}`
`=sqrt{(137-88)(137+88)}`
`=sqrt{49.225}`
`=7.15`
`=105`
`d) sqrt{192^2-111^2}`
`=sqrt{(192-111)(192+111)}`
`=sqrt{81.303}`
`=9sqrt{303}`
`e) sqrt{27/25}. sqrt{44/189}. sqrt{700/99}`
`=sqrt{27/25. 44/189. 700/99}`
`=sqrt{16/9}`
`=4/3`
`f) sqrt{9-sqrt{17}}.sqrt{9+sqrt{17}`
`=sqrt{81-17}`
`=sqrt{64}`
`=8`
`g) (2sqrt{3}-3sqrt{2})(2sqrt{3}+3sqrt{2})`
`=12-18`
`=-6`