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I have been stuck on a question in my math book for days and I have tried every website and video on youtube but none of them were helpful. There's a cubicle number as 3 radical 54 which simplifies, according to my guide book, to cubicle number 9 radical 2. I know in order to simplify them we have to multiply the prime factors of the number 54 but how it gets to 9 radical 2 is vague to me. I'd be grateful if anyone could explain this to me in the most simple terms and get me out of this confusion.

I have uploaded the image of the expression to more clarify my question.

https://pasteboard.co/HmNbIjN.jpg

mathquest3324
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  • For future: Where did you get the word "cubicle number"? The number that you have in the picture is a cube root (which, indeed, sounds a bit similar) – Matti P. May 25 '18 at 09:51

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Are you asking why $3 \sqrt[3]{54} = 9 \sqrt[3]{2}$? If so, it is because

  • $54=2\times 3^3$ and
  • $\sqrt[3]{3^3}=3$ so
  • $\sqrt[3]{54}=\sqrt[3]{2\times 3^3}=3\sqrt[3]{2}$ and
  • $3 \times 3=9$
Henry
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  • Do you multiply the product of two radicals in the last part? – mathquest3324 May 25 '18 at 10:41
  • $3 \times \sqrt[3]{54} = 3 \times \sqrt[3]{2 \times 3^3} = 3 \times \sqrt[3]{2} \times \sqrt[3]{3^3} = 3 \times \sqrt[3]{2} \times 3 = 9 \times \sqrt[3]{2} $ – Henry May 25 '18 at 13:27