Question
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
Answers
GPT 3.5
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.
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.