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`# Ly`

`a)`

        `4 sqrt28 - 5 sqrt63 - 3sqrt112 - 2 sqrt175`

`= 4 . sqrt{2^2 . 7} - 5 sqrt{3^2 . 7} - 3 sqrt{4^2 . 7} - 2 sqrt{5^2 . 7}`

`= 4 . 2 sqrt7 - 5. 3sqrt7 - 3. 4sqrt7 - 2. 5sqrt7`

`= 8sqrt7 - 15sqrt7 - 12sqrt7 - 10sqrt7`

`= -29sqrt7`

`b)`

             `4sqrt3 - 5sqrt12 + 3sqrt27 - 2sqrt48`

`= 4sqrt3 - 5 . sqrt{2^2 . 3} + 3. sqrt{3^2 . 3} - 2. sqrt{4^2 . 3}`

`= 4sqrt3 - 5. 2sqrt3 + 3. 3sqrt3 - 2. 4sqrt3`

`= 4sqrt3 - 10sqrt3 + 9sqrt3 - 8sqrt3`

`= -5sqrt3`

`c)`

               `(sqrt28 + 3sqrt63) . sqrt7`

`= (sqrt{2^2 . 7} + 3. sqrt{3^2 . 7}) . sqrt7`

`= (2sqrt7 + 3. 3sqrt7) . sqrt7`

`= (2sqrt7 + 9sqrt7) . sqrt7`

`= 11sqrt7 . sqrt7`

 `= 11. 7`

`= 77`

`d)`

             `(sqrt8 + 3sqrt18 - sqrt50) : sqrt2`

`= (sqrt{2^2 . 2} + 3. sqrt{3^2 . 2}- sqrt{5^2 . 2}) : sqrt2`

`= (2sqrt2 + 3. 3sqrt2 - 5sqrt2) : sqrt2`

`= (2sqrt2 + 9sqrt2 - 5sqrt2) : sqrt2`

`= 6sqrt2 : sqrt2`

`= 6`