My answer is yes an no. First I have not seen your gel but there is always small size RNA at the bottom of a gel, those are small transcripts but also small rRNA such as the 5,8S, however a high intensity smear is something different. A high intensity smear is generally a sign of degradation and I wouldn't do cDNA from those RNA. However some tissue often yield smear-like image but those are not RNAs but chemical compounds co-purifying with your RNA. I have had this problem from very young (green) tomato and I know potato tuber yield a similar features. CTAB can help but does not solve it. 

In short, my answer is, if it is degradation do not do cDNA from your RNA but depending on your tissue it may be an artifact looking like a degradation.

I completely agree with Hugo. From your description it is difficult to say if this smear is normal or indeed a strong degree of degradation.

If you have access to an Agilent Bioanalyzer, you can actually test the quality of your samples. Based on the size distribution, it will give you a RNA Integrity Number (RIN). Depending on the value, you can decide if it is worth it to make cDNA (for instance RT-qPCR requires lower quality than RNA-seq).

See more info here: http://www.genomics.agilent.com/article.jsp?pageId=2181

I fully agree with with both thoughtful answers.

As to the 5.8S rRNA argument: It is less visible if you do the run with EtBr in the gel only (as many people do) since it slowly migrates toward the anode. So, if you had EtBr in the buffer chamber as well, the fluorescence towards the bottom may indeed be the small rRNA.

Another sign of contamination by trace amounts of RNAse is a decrease in the ~ 2.5:1 fluorescence ratio between 28S vs. 18S rRNA. The former is a bit more susceptible to being cut. 

If you get indications of RNA degradation it is best to throw the sample away. There is no way to 'rescue' the intact molecules. 

Hello everyone thank you so much for your answers I loaded RNAs again and here is a picture of my gel. I couldn't find any smear band today but I wonder what is it between 28S and 18S band on the far right.

I am sorry to say so but your RNA shows clear signs of degradation.

For reference (quick Google) see e.g. Fig 2 in

https://www.researchgate.net/publication/43342792_Mitomycin_C_inhibits_ribosomal_RNA_A_novel_cytotoxic_mechanism_for_bioreductive_drugs/figures?lo=1

top: how it should look, bottom: *slightly* degraded - intermediates are visible

Article Mitomycin C inhibits ribosomal RNA: A novel cytotoxic mechan...