how do you know when you have to divide or multiply by the square root of two or the square root of 3?

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I'm not sure anyone understands you, but you normally multiply when going from a leg to the hypotenuse, and you divide when going from the hypotenuse to the leg. This is with the square root of 2. You can use the square root of 3 in different problems depending on the problem and equation. Hope that clarified things.