Analyze Robin’s reasoning in her answer to the test question about rational or irrational numbers. Does she have a deep understanding of rational and irrational numbers? Does her reasoning make sense? If not, what misconceptions does she have about this topic?

QUESTION: Is 130 rational or irrational? Where would 130 be located on a number line? Explain your reasoning.

ROBIN’S ANSWER: 130 is a rational number because 130 is even. All rational numbers are even and irrational numbers are odd when the numbers are under the square root sign. The square root sign is the opposite of squaring a number. Squaring a number is the same as raising it to the 2nd power. So, to find the value of a number under the square root sign, you divide it by 2. So, 130÷2 is 65. The answer is 65.

Rational number are those numbers that can be represented in the form of [tex]P/Q[/tex] where p and q are integers and q is a non zero denominator like [tex]3/2[/tex], [tex]5/8[/tex] etc.

Irrational number are those numbers that cannot be expressed in the form of [tex]P/Q[/tex] like [tex]\sqrt{2}[/tex], [tex]\sqrt{5}[/tex] etc.

1) 130 is a rational number because it is even: This is not true because rational number has nothing to do with the number being even or odd it should be of the form [tex]P/Q[/tex] with non zero denominator

2)All rational numbers are even and all irrational number are odd under square root: its false because of the same reason stated above.

3) The square root sign is the opposite of squaring a number: true because square root hold a power of 1/2 and squaring is raising it to the power of 2

4) TO find the value of number under the square root we divide it by 2: false because square root means raising the given number to the power of 1/2 and not diving it by 2

Hence, 130 will be plotted to the right hand side of the number line