Question

How do you simplify this? `" "sqrt(3) + sqrt(1/3)`

Answer 1

`sqrt3+sqrt(1/3)=4/sqrt3`

Explanation:

`sqrt3+sqrt(1/3)`

`sqrt3=3/sqrt3=`

`sqrt(1/3)=1/sqrt3`

`sqrt3+sqrt(1/3)=3/sqrt3+1/sqrt3`
`=(3+1)/sqrt3=4/sqrt3`
Thus,

`sqrt3+sqrt(1/3)=4/sqrt3`

Answer 2

`=4/3 sqrt3`

Explanation:

You can write the square root of the fraction as separate roots:

`sqrt3 + color(blue)(sqrt(1/3)) = sqrt3 + color(blue)(sqrt1/sqrt3)`

`sqrt3 + 1/sqrt3" "larr` rationalise the denominator

`=sqrt3 +1/sqrt3 xx sqrt3/sqrt3`

`=sqrt3 +sqrt3/3" "larr` factor out `sqrt3`

`=sqrt3(1+1/3)`

`=4/3 sqrt3`

Answer 3

`sqrt3+ sqrt(1/3)` is not an equation and, therefore, cannot be solved but it can be rationalized.

Explanation:

`sqrt3+ sqrt(1/3)`

Separate the second term into a radical over a radical:

`sqrt3+ sqrt1/sqrt3`

Multiply the second term by 1 in the form of `sqrt3/sqrt3`

`sqrt3+ sqrt1/sqrt3sqrt3/sqrt3`

Because of `sqrt3sqrt3=3`: the denominator becomes 3:

`sqrt3+ sqrt3/3`

Multiply the first term by 1 in the form of `3/3`:

`(3sqrt3)/3+ sqrt3/3`

The two fractions can be combined over the common denominator:

`(3sqrt3+ sqrt3)/3`

Add the terms in the numerator

`(4sqrt3)/3`

The above is the rationalized and simplified form.