Answer:
A rational number is a number that can be expressed as a fraction (the ratio of two integers).
Integer: A whole number that can be positive, negative, or zero.
To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:
[tex]\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}[/tex]
[tex]\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}[/tex]
[tex]\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}[/tex]
[tex]\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}[/tex]
Therefore, [tex]\sf \sqrt{12.1}[/tex] is not a rational number.
