Answer:
[tex] 16k\sqrt{2} [/tex]
or
[tex] 16|k|\sqrt{2} [/tex]
Step-by-step explanation:
Assume k is non-negative.
[tex] \sqrt{512k^2} = [/tex]
[tex] =\sqrt{256 \times 2} \times \sqrt{k^2} [/tex]
[tex] = 16\sqrt{2} \times k [/tex]
[tex] = 16k\sqrt{2} [/tex]
If you do not assume k is non-negative, then you must use absolute value, and you get:
[tex] = 16|k|\sqrt{2} [/tex]
