Question

Show that 12/radical 8 =3 radical 2​

Answer 1

see explanation

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Given

`(12)/(√(8) )`

To rationalise the denominator multiply the numerator/ denominator by
`√(8)`, thus

`(12)/(√(8) )` ×
`(√(8) )/(√(8) )`

=
`(12√(8) )/(8)`

`√(8)` =
`√(4(2))` = 2
`√(2)`, thus

=
`(12(2)√(2) )/(8)`

=
`(24√(2) )/(8)`

= 3
`√(2)` ← as required