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The speed of sound c in a gas depends on among other things on the pressure on the gas, the density and probably, possibly on their viscosity. Determine c-

My Variable list:

Pressure p ML^-1T^-2

Density ρ ML^-3

Speed v LT^-1

My matrix:

| | M | L | T |

| p | 1 | -1 | -2 |

| ρ | 1 | -3 | 0 |

| v | 0 | 1 | -1 |

after a couple of row reductions i got it to be:

k = P/(ρv^2) (pi=k)(k = constant)

The answer should be v = k(P/ρ)^(1/2)

I'm doing it right?