Victoria is finding the value of n for the equation 3 square root 14 1/6 = 14 1/n Victoria writes 3 square root 14 1/6 = (14 1/6)^3 = 14 3/6= 14 1/2. So n =2 is Victoria correct? Explain your answer and show your work in horizontal form
To determine if Victoria is correct, we need to evaluate the equation step by step.
The equation is: 3√(14 1/6) = 14 1/n
First, let's simplify 14 1/6 as an improper fraction:
14 1/6 = 14 + 1/6 = 14 + 1/6 = (14*6 + 1)/6 = 85/6
Now we can rewrite the equation:
3√(85/6) = 14 1/n
To simplify, we find the cube root:
3√(85/6) = (85/6)^(1/3)
To rationalize the denominator, we cube both the numerator and denominator:
(85/6)^(1/3) = (85/6)^(1/3) * (6^2)/(6^2) = (85 * 6^2)/(6^3) = (85 * 36) / 216 = 85/6
Now the equation becomes:
3√(85/6) = 14 1/n
Comparing the simplified equation, it is clear that Victoria's calculation is incorrect. The value of the left side is 85/6, not 14 1/2.
Therefore, Victoria's conclusion that n=2 is incorrect.