Question

Determine the square root of the polynomial using factorisation method: $\sqrt{\frac{81(x+y{)}^2(x-y{)}^8}{9(x-y{)}^4}}$ = ?

• A. $\left|\right(x+y\left)\right(x-y{)}^2|$
• B. $3\left|\right(x+y\left)\right(x-y{)}^2|$
• C. $3\left|\right(x+y\left)\right(x-y{)}^4|$
• D. $\left|3\right(x+y\left)\right(x-y{)}^2|$

Answer 1

The correct option is B $3\left|\right(x+y\left)\right(x-y{)}^2|$

$\sqrt{\frac{81(x+y{)}^2(x-y{)}^8}{9(x-y{)}^4}}$
$=$ $\sqrt{{\left(\frac{9(x+y)(x-y{)}^4}{3(x-y{)}^2}\right)}^2}$
$=$ $\sqrt{{\left(\frac{9(x+y)(x-y{)}^2}{3}\right)}^2}$
$=$ $\frac{9}{3}\sqrt{\left(\right(x+y\left)\right(x-y{)}^2{)}^2}$
$=$ $3\left|\right(x+y\left)\right(x-y{)}^2|$