How to simplify cubicle numbers?

Question

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

Answer 1

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
• $3 \times 3=9$