Put the quinoa and 360ml water in a saucepan set over a high heat and bring to the boil. Reduce the heat to low, cover with a lid and simmer for 12 minutes, or until cooked. Drain, return to the pan, cover and leave to steam for 10 minutes, then cool completely.
Whisk together the lime juice, fish sauce, vinegar, oil and soy sauce in a bowl. Adjust the levels of lime juice and fish sauce to taste.
Peel the mango and cucumber into thin ribbons and add to a bowl with the radishes, quinoa and mint. Pour over the dressing, toss to combine and serve.