By the use of nanodrop,you can measure both quality and quantity of extracted DNA.

By real time PCR. Biophotometry no works wel for DNA extracted by chelex.

Actually, by using nanodrop, you can do it. However, you also have to realize that the DNA concentration which is produced by using Chelex is commonly lower than the concentration which is produced by using another method. It happens since usually there are still a lot of debris mixed together with the DNA molecules. So, do you really need to measure it? I suggest that you should check directly the DNA molecule as the extraction result by using PCR process.

This is from my personal experience. I've obtained DNA samples using Chelex method and I quantified it using Nanodrop, but my results were inconsistent. Some samples showed zero DNA but the gel electrophoresis image showed band. So I directly went for PCR for amplifying my gene of interest and found my products amplified nicely and with exact bp length as I was expecting it to be. So I suggest you to try PCR directly.

We use Nanodrop to know the quantity of DNA. The addition of the drop on the lens must be in vertical position. My under graduate students in their research got best results in measuring with nanodrop. 

First of all thank you all. I have been going for PCR for quite sometime, however, not been able to get consistent result. I have never tried Nanodrop before so will try if its help to me.

Qubit (HS DNA kit) can detect lower concentrations than Nanodrop, and it is more accurate because it is a flourometric assay.

Qubit only measures double stranded DNA and chelex extractions produce single stranded- i think that Nanodrop is the best bet- as you need a standard to compare against in qpcr. If you recombine the extractions ot make double stranded DNA Qubit is, however, a lot more accurate!