to find the product of (-2\\sqrt{20k})(5\\sqrt{8k^{3}}), first write using a single radical. which…

to find the product of (-2\\sqrt{20k})(5\\sqrt{8k^{3}}), first write using a single radical. which expression is equivalent to the given product?\n-10\\sqrt{160k^{3}}\n-10\\sqrt{160k^{4}}\n3\\sqrt{28k^{4}}\n3\\sqrt{28k^{3}}\ndone

to find the product of (-2\\sqrt{20k})(5\\sqrt{8k^{3}}), first write using a single radical. which expression is equivalent to the given product?\n-10\\sqrt{160k^{3}}\n-10\\sqrt{160k^{4}}\n3\\sqrt{28k^{4}}\n3\\sqrt{28k^{3}}\ndone

Answer

Explanation:

Step1: Multiply the coefficients

Multiply -2 and 5: $(-2)\times(5)= - 10$.

Step2: Multiply the radicands

Multiply $\sqrt{20k}$ and $\sqrt{8k^{3}}$. Using the property $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$, we have $\sqrt{20k\times8k^{3}}=\sqrt{160k^{4}}$.

Step3: Combine the results

The product is $-10\sqrt{160k^{4}}$.

Answer:

$-10\sqrt{160k^{4}}$