Find the square root of $$x^2+10+\frac{(-20x-15)}{x^2+4x+4}$$
I tried to do by taking the denominator across the entire expression, because the denominator was already a perfect square, but I ended up with an expression in the numerator which had no real roots: $$\frac{x^4+4x^3+14x^2+20x+25}{x^2+4x+4}$$
Is there a simpler method which I am missing? Thanks for any help :-)
$(x^2+ax+5)^2=x^4+2ax^3+(a^2+10)x+10ax+25=x^4+4x^3+14x^2+20x+25$ when $a=2$.