Solve for v...?

Question

p = 1 / [ √(1 - (v^2/c^2)) ]

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Answer 1

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p = 1 / [ √(1 - (v^2/c^2)) ]

p [ √(1 - (v^2/c^2)) ] = 1

squaring on both sides to get rid of the sq.root

p^2 (1- (v^2/c^2)) = 1

1 - (v^2/c^2) = 1 / p^2

v^2/c^2 = 1 - (1/p^2)

v^2 = c^2 (1 - (1/p^2))

Apply sq.root on both sides to get v

v = √ (c^2 (1 - (1/p^2)))

v = c √ (1 - (1/p^2))

Answer 2

p = 1 / [ √(1 - (v^2/c^2)) ]

1/p = [ √(1 - (v^2/c^2)) ]

(1/p)^2 = 1- (v^2/c^2)

(1/p)^2 - 1 = -v^2/c^2

c^2[(1/p)^2 - 1] = -v^2

v^2 = [c^2 - c^2/p^2]

v = +/- sqrt[c^2 - c^2/p^2]

Answer 3

p = 1 / [ √(1 - (v²/c²)) ]

Square this equation,

p² = 1 / (1-v²/c²)

Cross multiply

1-v²/c² = (1/p²)

v²/c² = 1 - (1/p²)

v² = c² [1 - (1/p²)]

take square root

v = c √[1 - (1/p²)]