Given that the exact value of sin(θ) = 3/5, use the fact that cos(θ) = squareroot(1 - sin^2(θ)) to find cos(θ) as a fraction or surd without finding θ first.

How do you answer this? I have to show step by step, this is what I did:

sin(θ) = 3/5
cos^2(θ) = 1 - sin^2(θ)
squareroot(cos^2(θ)) = squareroot(1 - sin^2(θ))
cos(θ) = squareroot(1 - sin^2(θ))
cos(θ) = squareroot(1 - (3/5)^2)
cos(θ) = squareroot(1 - 9/25)
cos(θ) = squareroot(25/25 - 9/25)
cos(θ) = squareroot(16/25)
cos(θ) = squareroot(16) / squareroot(25)
cos(θ) = 4/5

Is this correct?