$${\sqrt{{\mathtt{20}}}}$$ is called an irrational number. That means that it cannot be expressed as a fraction or as a decimal.
Ansy answer that your calculator gives you is just an estimate. All the digits on your calculator will be used up because the digits just keep going on for ever and there is never any pattern.
You can simplify it to
$${\sqrt{{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{5}}}} = {\mathtt{4.472\: \!135\: \!954\: \!999\: \!579\: \!4}}$$
$${\sqrt{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}} = {\mathtt{4.472\: \!135\: \!954\: \!999\: \!579\: \!4}}$$
$${\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}} = {\mathtt{4.472\: \!135\: \!954\: \!999\: \!579\: \!4}}$$
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