Question

What is the square root of the polynomial $\frac{x^2+10x+25}{(x+5{)}^4}$ using factorisation method?

• A. $\left|\frac{1}{x+5}\right|$
• B. $\frac{1}{x+5}$
• C. $\left|\frac{1}{(x+5{)}^2}\right|$
• D. $\frac{x}{x+5}$

Answer 1

The correct option is A $\left|\frac{1}{x+5}\right|$

$\sqrt{\frac{x^2+10x+25}{(x+5{)}^4}}$
Factor of $x^2+10x+25=(x+5{)}^2$
$\sqrt{\frac{x^2+10x+25}{(x+5{)}^4}}=\sqrt{\frac{(x+5{)}^2}{(x+5{)}^4}}$
$=$ $\sqrt{\frac{1}{(x+5{)}^2}}$
$=$ $\left|\frac{1}{x+5}\right|$