Question

Simplify 7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54 . (1 point) 11 square root of 6 end root minus 7 square root of 12 11 square root of 3 end root minus 7 square root of 6 negative 3 square root of 9 4 square root of 9

Answer 1

11
`√(3)` - 7
`√(6)`

Explanation:

using the rule of radicals

`√(ab)` =
`√(a)` ×
`√(b)`

then simplifying the following

`√(48)`

=
`√(16(3))`

=
`√(16)` ×
`√(3)`

= 4
`√(3)`

and

`√(54)`

=
`√(9(6))`

=
`√(9)` ×
`√(6)`

= 3
`√(6)`

given

7
`√(3)` - 4
`√(6)` +
`√(48)` -
`√(54)` ( using the above simplifications )

= 7
`√(3)` - 4
`√(6)` + 4
`√(3)` - 3
`√(6)` ← collect like radicals

= 11
`√(3)` - 7
`√(6)`