# Finding square root of given expression

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 :-)

• @Bernard, you are right, I didn't think about that! I have edited it – Fasal123 Apr 8 '18 at 11:43
• But it has a root easily explicit. – Piquito Apr 8 '18 at 11:47

$(x^2+ax+5)^2=x^4+2ax^3+(a^2+10)x+10ax+25=x^4+4x^3+14x^2+20x+25$ when $a=2$.