Question

Evaluate `sqrt(6)-sqrt(3)` when `sqrt(2)=1.414` ?

Answer 1

`0.414sqrt3`
or
`0.717`

Explanation:

`sqrt6-sqrt3`

`=sqrt2sqrt3-sqrt3`

`=sqrt3(sqrt2-1)`

`=sqrt3(1.414-1)`

`=0.414sqrt3`

Note: `sqrt3 approx 1.732`
Therefore,

`sqrt6-sqrt3`

`=0.414(1.732)`

`=0.717`

Answer 2

`sqrt6-sqrt3=color(blue)(0.414sqrt3`

Explanation:

Given:

`sqrt6-sqrt3`

Prime factorize `sqrt6`.

`sqrt(2xx3)-sqrt3`

Apply rule: `sqrt(ab)=sqrt(a)sqrt(b)`

`sqrt2sqrt3-sqrt3`

Substitute `1.414` for `sqrt2`.

`1.414sqrt3-sqrt3`

The coefficient of `sqrt3` is understood to be `1`.

`sqrt3=1xxsqrt3`

`1.414sqrt3-1sqrt3`

`0.414sqrt3`