Question

Combine the following expressions.

Answer 1

second option

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Simplifying the radicals

`\sqrt{27x^(3) }`

=
`√(9(3)x^2.x)`

=
`√(9)` ×
`√(3)` ×
`√(x^2)` ×
`√(x)`

= 3 ×
`√(3)` × x ×
`√(x)`

= 3x
`√(3x)`

-------------------------------

`\sqrt{12x^(3) }`

=
`√(4(3)x^2.x)`

=
`√(4)` ×
`√(3)` ×
`√(x^2)` ×
`√(x)`

= 2 ×
`√(3)` × x ×
`√(x)`

= 2x
`√(3x)`

---------------------------------------

Thus

3 × 3x
`√(3x)` - 2 × 2x
`√(3x)`

= 9x
`√(3x)` - 4x
`√(3x)`

= 5x
`√(3x)`