# Monthly maths problem: March 2020

Thursday 12th March 2020

Find a polynomial with integer coefficients which has as a root $$\sqrt{2}+\sqrt{3}$$.

We could try: $(x-\sqrt{2}-\sqrt{3}) (x+\sqrt{2}+\sqrt{3}) (x-\sqrt{2}+\sqrt{3}) (x+\sqrt{2}-\sqrt{3})$

$=(x^2+5+2\sqrt{6}) (x^2+5-2\sqrt{6})$

$(x^2+5)^2-24=x^4+10x^2+1$