Question

Which expression is equivalent to 4√6/3

Answer 1

`(4)/(3){\sqrt3}`

Explanation:

The question seem incomplete;

The full question is

Which expression is equivalent to 4√6/3√2

Given

4√6/3√2

Required

Find equivalent

`4\sqrt6/3\sqrt2`

Rewrite Expression

`(4\sqrt6)/(3\sqrt2)`

Expand the above expression

`(4\ *\ \sqrt6)/(3\ * \ \sqrt2)`

Further split the fraction

`(4)/(3)\ *\ (\sqrt6)/(\sqrt2)`

Using rule of surds;

`(\sqrt a)/(\sqrt b) = \sqrt{(a)/(b)}`

So, the above expression becomes

`(4)/(3)\ *\ \sqrt{(6)/(2)}`

`(4)/(3)\ *\ {\sqrt3}`

`(4)/(3){\sqrt3}`

At this stage, the expression cannot be further simplified;

Hence, 4√6/3√2 =
`(4)/(3){\sqrt3}`