Question

simplify the radical expression.
$-21sqrt{20x^{13}}$

$-21sqrt{20x^{13}} = square$
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor the radicand

$\sqrt{20x^{13}} = \sqrt{4 \cdot 5 \cdot x^{12} \cdot x}$

Step2: Split into separate radicals

$\sqrt{4} \cdot \sqrt{5} \cdot \sqrt{x^{12}} \cdot \sqrt{x}$

Step3: Simplify each radical

$\sqrt{4}=2$, $\sqrt{x^{12}}=x^6$, so:
$2 \cdot x^6 \cdot \sqrt{5x}$

Step4: Multiply by the coefficient

$-21 \cdot 2x^6\sqrt{5x}$

Answer:

$-42x^6\sqrt{5x}$