Rationalising surds question grade 10

Question

I am a student and I need help answering answering this question. I don't know if I should get rid of the 6.

2)Rationalise and simplify

$$\frac{6}{3+\sqrt 40}$$

Thank you and help is appreciated

Answer 1

Multiply numerator and denominator by $3-2\sqrt{10}$ which gives $$\frac{6}{3+\sqrt 40}=\frac{6(3-2\sqrt{10})}{(3+2\sqrt 10)(3-2\sqrt{10})}=\frac{18-12\sqrt{10}}{9-40}=\frac{12\sqrt{10}-18}{31}$$

Since $(a+b)(a-b)=a^2-b^2$