Floating floor: should I staple down underlayment?

No, I don't, but I tape the seams together.

From Hosking Hardwood:

There are a multitude of underlayments available for floating installations. They range from simple foam pads to foam pads with a plastic moisture barrier attached to dense felt-like underlayments with remarkable sound absorption properties. Foam pads are typically thinner and their sole purpose is to add a little cushion. Foam pads with moisture barriers attached are also on the thinner side but also offer that moisture protection. The denser underlayment pads (usually a felt like material) are typically a bit thicker and offer more support and insulation because of there dense nature.

Some hardwood and laminate manufacturers make their own underlayments for floating applications, which they recommend for use with their products. However, in most cases, any industry approved underlayment will get the job done. It's important, prior to installation, to read the specific flooring manufacturer's installation instructions. If they require use of their brand specific underlayment in order for their warranty to be effective, it's always a good idea to acquiesce.

Installation of underlayment for a floating floor is very simple. Underlayments typically come in rolls. After subfloor prep, simply roll out the underlayment. Many underlayments these days have self-stick overlap flaps for connecting multiple sections of underlayment together. If the underlayment you are using doesn't have these, you can simply use duct tape to secure the edge of one portion of underlayment to the other. (Some flooring manufacturers will sell seam tape, but, really, duct tape works just as well.)

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