If the cash is a little more than the nisaab, does one have to pay zakaah on this additional amount?

If the cash reaches the nisaab and one year has passed since it was acquired, it is obligatory to pay zakaah on the entire amount, at the rate of 2.5%. 

It says in Haashiyat al-‘Adawi ‘ala al-Kifaayah (1/481): No zakaah is due on gold if it is less than twenty dinars. If the number of dinars reaches twenty, then half a dinar must be given in zakaah. If there are more than twenty dinars, he should give the same percentage as zakaah, even if it is a small amount. End quote. 

Ibn Muflih said in al-Furoo‘ (2/322): Zakaah is obligatory on any amount of money that exceeds the nisaab, at the same rate. End quote. 

That is proven by the hadeeth from the Prophet (blessings and peace of Allah be upon him). 

Abu Dawood narrated (1572) from ‘Ali (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “You do not have to pay anything on gold unless you have twenty dinars; if you have twenty dinars and one year has passed since acquiring them, then half a dinar is due on them, and if there is more than that, then work it out on the same basis.” 

Classed as saheeh by al-Albaani (may Allah have mercy on him) in Saheeh Abi Dawood. 

And Allah knows best.