Question

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

Answer 1

Answer:

  $1-\dfrac{2}{3}\sqrt{3}$

Step-by-step explanation:

Maybe you want to simplify ...

  $(1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}$

Multiply numerator and denominator by the 'conjugate' of the denominator:

  $(1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}=\dfrac{(1-\sqrt{3})(3-\sqrt{3})}{9-3}=\dfrac{3-4\sqrt{3}+3}{6}\\\\\boxed{1-\dfrac{2}{3}\sqrt{3}}$