Victoria is finding the value of n for the equation 1416−−−√3=141n

Question

Victoria writes 1416−−−√3=(1416)3=1436=1412
so n=2

Answer 1

This is incorrect. Let's solve it correctly:

We have the equation:

$\sqrt{1416} = 141n$

To solve for $n$, we first simplify $\sqrt{1416}$:

$\sqrt{1416} = \sqrt{4 \cdot 354 = 2 \cdot \sqrt{354}}$

Now we have:

$2 \cdot \sqrt{354} = 141n$

Divide both sides by 141:

$\frac{2 \cdot \sqrt{354}}{141} = n$

Simplifying further:

$n = \frac{\sqrt{354}}{71}$

So the correct value of $n$ is $\frac{\sqrt{354}}{71}$.