Question

How do you simplify `sqrt14-sqrt2/7`?

Answer 1

`sqrt14-(sqrt2)=color(blue)((7sqrt14-sqrt2)/7`

Explanation:

Simplify:

`sqrt14-(sqrt2)/7`

In order to add or subtract fractions, they must have the same denominator; the least common denominator (LCD). The LCD for this expression is `7`.

Multiply `sqrt14` by `7/7` to get an equivalent fraction with `7` as the denominator. Since `7/7=1`, the numbers will change, but the value will remain the same.

`sqrt14xx7/7-(sqrt2)/7`

Simplify `sqrt14xx7/7` to `(7sqrt14)/7`.

`(7sqrt14)/7-sqrt2/7`

Combine the numerators.

`(7sqrt14-sqrt2)/7`

Answer 2

`sqrt14-sqrt2/7=sqrt2(sqrt7-1/7)`

Explanation:

`sqrt14-sqrt2/7`
`=sqrt7*sqrt2-sqrt2/7`
`=sqrt2(sqrt7-1/7)`