The square root of the cube root of a number is 8. What is the square of the number?

Question

This is just a math riddle for extra credit.

Answer 1

8 is the sqrt of 64, which is the cube root of 262144. That number squared is in fact 8 to the 12th, as Michael pointed out. (But this way might be easier to understand.)

Answer 2

Hello, Apologies for the non-answer. I'm just learning this forum and somehow posted a blank answer box. Since you already have 2 excellent answers I will try again another day :) Dr. Fran

Answer 3

Take the cube-root first, then the square-root of the result.  It will be 8.

 

(x^1/3)^1/2 = 8

 

 

where x is the number.

 

Using rules of exponents,

 

x^1/6 = 8

 

 

Raise both sides of the equation by 12.

 

(x^1/6)¹² = 8¹²

 

x² = 8¹²