Question

Find the square root of the polynomial using factorisation method: $\frac{(x^2-81{)}^2}{(x+9{)}^4}$.

• A. $(x-9{)}^2$
• B. $\left|\right(x-9\left)\right|$
• C. $\left|\right(x-9{)}^2|$
• D. $\left|\right(x+9{)}^2|$

Answer 1

The correct option is C $\left|\right(x-9{)}^2|$

$\sqrt{\frac{(x^2-81{)}^2}{(x+9{)}^4}}$
Factor of $x^2-81=(x+9)(x-9)$
$=$ $\sqrt{{\left(\frac{\left(\right(x+9\left)\right(x-9){)}^2}{(x+9{)}^2}\right)}^2}$
$=$ $\sqrt{\left(\right(x-9{)}^2{)}^2}$
$=$ $\left|\right(x-9{)}^2|$