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Nady [450]
1 year ago
15

Which of the following is NOT a rational number?

Mathematics
1 answer:
makvit [3.9K]1 year ago
5 0

Answer:

A <u>rational number</u> is a number that can be expressed as a fraction (the ratio of two integers).  

<u>Integer</u>:  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:

\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}

\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}

\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}

\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}

Therefore, \sf \sqrt{12.1} is not a rational number.

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