Question

Which of the following is NOT a rational number?

A
√121
B
√12.1
C
√1.21
D
√0.0121

Answer 1

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:

`√(121)=√(11^2)=11=(11)/(1) \quad \leftarrow \textsf{rational}`

`√(12.1)=\sqrt{(1210)/(100)}=(√(1210))/(√(100))=(√(121\cdot 10))/(10)=(√(121)√(10))/(10)=(11√(10))/(10) \leftarrow \textsf{not rational}`

`√(1.21)=\sqrt{(121)/(100)}=(√(121))/(√(100))=(√(11^2))/(√(10^2))=(11)/(10) \leftarrow \textsf{rational}`

`√(0.0121)=\sqrt{(121)/(10000)}=(√(121))/(√(10000))=(√(11^2))/(√(100^2))=(11)/(100) \leftarrow \textsf{rational}`

Therefore,
`\sf √(12.1)` is not a rational number.