Question

Simplify (1-√3)(⅓+√3) leaving your answer in the form p+q√3​

Answer 1

`(-8 +2√(3) )/(3)`

Explanation:

When working with surds we need to take note of the roots present there.

To expand this equation we can do it the following way noting that √3 X √3 = 3

Expanding (1-√3)(⅓+√3)

1 X 1/3 = 1/3

1 X √3 = √3

-√3 X 1/3 =-√3/3

√3 X √3 = 3

hence, expanding the equation, we have

1/3 + √3 -√3/3 + 3

We can simply group the like terms and add them up.

[1/3 +3] +[√3-√3/3]

10/3 +
`(2√(3) )/(3)`

=
`(-8 +2√(3) )/(3)`