Question

Which Choice is equivalent to the quotient shown here when x is greater or equal to 0

Answer 1

C

Explanation:

using the rules of radicals

•
`(√(a) )/(√(b) )` ⇔
`\sqrt{(a)/(b) }`

•
`√(a)` ×
`√(b)` ⇔
`√(ab)`

given
`√(27x)` ÷
`√(48)`

simplifying the radicals

`√(27x)` =
`√(9(3)x)` = 3
`√(3x)`

`√(48)` =
`√(16(3))` = 4
`√(3)`, hence

`(3√(3x) )/(4√(3) )`

=
`(3√(x) )/(4)` → C

Answer 2

`\sqrt{ (27x)/(48) } = \sqrt{ \frac{ {3}^(3)x}{ {2}^(4) * 3 } } = \sqrt{ \frac{ {3}^(2)x }{ {2}^(4) } } = (3 √(x) )/(4)`