Question

Using factorization method, find the square root of $\sqrt{(x^2+10x-39{)}^2}$.

• A. $\left|\right(x-3\left)\right(x-13\left)\right|$
• B. $\left|\right(x-3\left)\right(x+13\left)\right|$
• C. $\left|\right(x+3\left)\right(x+13\left)\right|$
• D. $(x-3)(x+13)$

Answer 1

The correct option is B $\left|\right(x-3\left)\right(x+13\left)\right|$

$\sqrt{(x^2+10x-39{)}^2}$

$=$ $\sqrt{(x^2+10x-39{)}^2}$

$=\sqrt{x^2+13x-3x-39}$

$=\sqrt{(x-3)(x+13)}$

Factor of $x^2+10x-39=(x-3)(x+13)$
$=$ $\sqrt{\left(\right(x-3\left)\right(x+13){)}^2}$
$=$ $\left|\right(x-3\left)\right(x+13\left)\right|$