Question

1. circle the irrational number in the list below. 7.27 $\frac{5}{9}$ $sqrt{15}$ $sqrt{196}$

Explanation:

Step1: Define rational and irrational

A rational number can be written as $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. An irrational number cannot be written as a fraction.

Step2: Analyze $7.\overline{27}$

$7.\overline{27}$ is a repeating - decimal. Let $x = 7.\overline{27}$, then $100x=727.\overline{27}$, and $100x - x=727.\overline{27}-7.\overline{27}$, $99x = 720$, $x=\frac{720}{99}=\frac{80}{11}$, so it is rational.

Step3: Analyze $\frac{5}{9}$

It is already in the form of $\frac{p}{q}$ ($p = 5$, $q = 9$, both are integers and $q
eq0$), so it is rational.

Step4: Analyze $\sqrt{15}$

The square - root of a non - perfect square number is irrational. 15 is not a perfect square (since there is no integer $n$ such that $n^2=15$), so $\sqrt{15}$ is irrational.

Step5: Analyze $\sqrt{196}$

$\sqrt{196}=14$ (because $14\times14 = 196$), and $14=\frac{14}{1}$, so it is rational.

Answer:

$\sqrt{15}$