The nearest starts to Earth are approximately 4.0 lightyears away. How fast woul

Question

The nearest starts to Earth are approximately 4.0 lightyears away. How fast would you have to travel in a spaceship to cause that distance to shrink to 1.5 lightyears?

I get most of this, I'm having trouble (or doing something incorrect with the math).

Lp = 4.00 ly. therefore, if L = 1.50 ly, then

L =Lp sqrt 1 - v^2/c^2

L/Lp = sqrt 1 - v^2/c^2

0.375 = sqrt 1 - v^2/c^2

I tried squaring both sides and I'm messing something up from her to the end.

and end up with v/c = 0.927 or v = 0.927c WHICH IS THE ANSWER

I'm trying to square both sides and I keep coming up with 0.7 or 0.3. Thanks!

Explanation / Answer

I got correctly only

0.140625=1-v^2/c^2

v^2/c^2=0.859375

Now taking square root on both sides,

So v/c=0.927

So v=0.927c

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