Victoria is finding the value of n for the equation 3/sqrt14 1/6 = 14 1/n
Victoria writes 3/sqrt 14 1/6 = (14 1/6)^3 = 14 3/6= 14 1/2 so n=2
Is Victoria correct? Justify your answer.
(3 points)
No, Victoria is not correct.
To solve the equation 3/sqrt(14) * 1/6 = 14 * 1/n, we have to simplify each side of the equation separately and then compare them.
On the left side:
1/6 can be simplified to 1 รท 6 = 1/6.
sqrt(14) cannot be simplified any further, so it remains as sqrt(14).
So the left side simplifies to 3/sqrt(14) * 1/6 = 3/(sqrt(14) * 6) = 3/6sqrt(14) = 1/2sqrt(14).
On the right side:
14 * 1/n simplifies to 14/n.
So now we have 1/2sqrt(14) = 14/n.
To find the value of n, we need to isolate n on one side of the equation. To do that, we can multiply both sides of the equation by n, which gives us:
n * (1/2sqrt(14)) = n * (14/n).
Simplifying the left side gives us (n/2sqrt(14)) and simplifying the right side gives us 14.
So now we have (n/2sqrt(14)) = 14.
To isolate n, we can multiply both sides of the equation by 2sqrt(14), which gives us:
2sqrt(14) * (n/2sqrt(14)) = 2sqrt(14) * 14.
Simplifying the left side gives us n, and simplifying the right side gives us 28sqrt(14).
So the final result is n = 28sqrt(14), not n = 2.
Therefore, Victoria's answer is not correct.