Question

Find a quadratic equation whose one root is square root of $-47+8\sqrt{-3}.$

Answer 1

If it is a square root of given quantity, then the given quantity can be broken into square of

$-47+8\sqrt{-3}=-47+2\times 4\sqrt{-3}\times 1=(4\sqrt{-3}{)}^2+1^2+2\times 4\times \sqrt{-3}\times 1=(1+4\sqrt{-3}{)}^2$

So, one root is $1+4\sqrt{-3}$

and other root is $1-4\sqrt{-3}$

So, equation is $x^2-2x+49=0$