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**PythagorasNeophyte** Thank you for your response, but I am looking for the **elements **of $\displaystyle B$ and $\displaystyle A\cap B $. Nonetheless, I am still dubious of how the element $\displaystyle x^2$ in the set $\displaystyle B$ could be substituted, so I'm stuck in listing the elements of set $\displaystyle B$. I also do not know why $\displaystyle A=\{x:0\le x\le 10\},$ and $\displaystyle B=\{x:0\le x^{2}<82\}.$ both have $\displaystyle x:0$ rather than $\displaystyle x:x$.