Question

Which expression is equal to 2√28 + 2√63? A: 13√7 B: 4√7 C: 10√7 D: 12√7

Answer 1

C

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Simplifying the radicals

`√(28)`

=
`√(4(7))`

=
`√(4)` ×
`√(7)` = 2
`√(7)`

and

`√(63)`

=
`√(9(7))`

=
`√(9)` ×
`√(7)` = 3
`√(7)`

Hence

2
`√(28)` + 2
`√(63)`

= 2(2
`√(7)` ) + 2(3
`√(7)` )

= 4
`√(7)` + 6
`√(7)`

= 10
`√(7)` → C