Simply, You cant! (with naked eye).

You can see protein when it precipitate/aggregate(same applies for DNA) and DNA may look (viscous)thread like bodies while lysing the cells. Proteins may form froth depends on concentration and buffer composition but not always the same!

Soluble (meaningful) DNA/protein needs to be checked with said appropriate methods.

Easiest way is a quick scan of your sample with the spectrophotometer

260 nM for DNA, 280 nM for protein

Simply, You cant! (with naked eye).

You can see protein when it precipitate/aggregate(same applies for DNA) and DNA may look (viscous)thread like bodies while lysing the cells. Proteins may form froth depends on concentration and buffer composition but not always the same!

Soluble (meaningful) DNA/protein needs to be checked with said appropriate methods.

If it is general knowledge question then I am agree that

Proteins may form froth while shaking solution and DNA not. If it is scientific then go for spectrophotometer assay.

Listen to Ananda. The question DID say 'naked eye' and 'no lab techniques'.

:)

It depends on what you mean by "lab techniques" (equipments ?). You can test the presence of proteins by adding NaOH and Copper sulfate ("Biuret reaction") to your solutions and compare the colour with a control solution made only with water.