What is the product of 8√16d • 2d√3? Simplify if possible.

Question

anonymous · Answer

What is the square root of 16?

anonymous · Answer

4

anonymous · Answer

Okay. Quick question: does that "d" next to your 16 also go under the square root is it outside of it?
$$\sqrt{16d}$$ or$$\sqrt{16} * d$$

anonymous · Answer

under?

anonymous · Answer

sorry I've been taking this test for 5 hours now... my head is in like a million different places so even simple questions i can't figure out.

anonymous · Answer

Well taking your mind off it for like 10 minutes to just go take a walk and get some fresh air or just watching TV for 10 minutes would probably help if you are so stressed. Being stressed blocks the brain from functioning normally.$$8 * \sqrt{16d} = 8*\sqrt{16}*\sqrt{d}=8*4*\sqrt{d}=32\sqrt{d}=32*d ^{1/2}$$ Because a square root just means that number taken to the power of 1/2. So then the rest of your problem turns into: $$32d ^{1/2} * 2d \sqrt{3} = (32*2)*(d ^{1/2}*d ^{1}) \sqrt{3} =64 d ^{1/2 + 1}=64d ^{3/2}$$

anonymous · Answer

I don't know if that's the easiest way to do it, maybe there's a better way. Do you have answers to choose from or are you just supposed to type in what you think it is?

anonymous · Answer

It can also be expressed as:$$64d ^{3/2}=64(d ^{3})^{1/2}=64 \sqrt{d ^{3}}$$

anonymous · Answer

my choices are
16d√3
32d√2d
64d√3d
2d√6d

anonymous · Answer

Oh okay then I just went too far. It's simpler than what I did. $$8 *\sqrt{16d} * 2d \sqrt{3}=8 * \sqrt{16} * \sqrt{d} * 2d \sqrt{3} = 8*4*\sqrt{d} * 2d \sqrt{3}$$ You can just multiply the square roots together then:$$32 * 2d * \sqrt{3d}$$

anonymous · Answer

$$32*2d*\sqrt{3d}=64d \sqrt{3d}$$

anonymous · Answer

My bad, my original answer was too much :P

anonymous · Answer

thanks so much.. really helped me out.. now just 2 or 3 questions left.

anonymous · Answer

Just remember that if you have two things being multiplied in a square root you can split them up into their own 2 separate square roots. And vice-versa: if you have two separate square roots being multiplied together you can put them under the same square root.$$\sqrt{a}*\sqrt{b}=\sqrt{ab}$$ $$\sqrt{ab}=\sqrt{a} * \sqrt{b}$$
Feel free to post more questions :)