How would I go about answering this problem (should be easy)?

Question

Im pretty weak at math but I need to know HOW to answer this problem, I already have the answer, but I need to know how to get the answer

Problem

4.1 x 10^-8 = 2.6 x 10^-8 / [1 – (v/c)^2]^1/2

Where c= 3 x 10^8
and I have to find v=?

Answer 1

4.1×10^(-8) = 2.6×10^(-8)/√(1-(v/c)²)

Multiply both sides by √(1-(v/c)²):

√(1-(v/c)²) × 4.1×10^(-8) = 2.6×10^(-8)

Divide by 4.1×10^(-8):

√(1-(v/c)²) = 26/41

Square both sides:

1-(v/c)² = 676/1681

Add (v/c)²-676/1681:

1005/1681 = (v/c)²

Take the square root of both sides:

v/c=√1005/41

Multiply by c:

v = c×√1005/41 ≈ 2.3×10^8 m/s

Answer 2

4.1 x 10^(-8) = 2.6 x 10^(-8) / √(1 - (v/c)^2)

4.1 x 10^(-8) * √(1 - (v/c)^2) = 2.6 x 10^(-8)

√(1 - (v/c)^2) = 2.6 x 10^(-8) / 4.1 x 10^(-8)

√(1 - (v/c)^2) = 2.6/4.1

1 - (v/c)^2 = (2.6/4.1)^2

(v/c)^2 = 1 - (2.6/4.1)^2

v/c = √(1 - (2.6/4.1)^2)

v = √(1 - (2.6/4.1)^2) * 3 x 10^8

v = 231963914.4 = 2.32 x 10^8 (approx)

Answer 3

4.1 x 10^-8 = 2.6 x 10^-8 / [1 – (v/c)^2]^1/2
move factors .. inverting them when you do
[ 1-(v.c)^2)]^1/2 = 2.6/4.1
square both sides
1 - (v/c)^2 = (2.6/4.1)^2
move terms .. changing sign when you do
(v/c)^2 = 1 - (2.6/4.1)^2
square root both sides
v/c = (1 - (2.6/4.1)^2 ) ^(1/2)
move c over
v = c (1 - (2.6/4.1)^2 ) ^(1/2)