For a spring-mass oscillator, if you triple the mass but keep the stiffness the same, by what numerical factor does the period change?

For a spring-mass oscillator, if you triple the mass but keep the stiffness the same, by what numerical factor does the period change? That is, if the original period was T and the new period is bT, what is b? It is useful to write out the expression for the period and ask yourself what would happen if you tripled the mass.