Question

Which choice is equivalent to the expression below? √27 - √12 + √48

A. 29√3
B. 9√3
c. 21√3
D. 5√3

Answer 1

D

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Simplifying each radical

`√(27)`

=
`√(9(3))` =
`√(9)` ×
`√(3)` = 3
`√(3)`

`√(12)`

=
`√(4(3))` =
`√(4)` ×
`√(3)` = 2
`√(3)`

`√(48)`

=
`√(16(3))` =
`√(16)` ×
`√(3)` = 4
`√(3)`

Then

3
`√(3)` - 2
`√(3)` + 4
`√(3)`

= 5
`√(3)` → D