Question

answer the question below. (2 points)

1. circle the real numbers below that are irrational.

\\( \frac { 2 } { 5 } \\)\t\\( \sqrt { 100 } \\)\t\\( \sqrt { 50 } \\)\t0.4545789\t\\( \pi \\)
use the lines below to explain why you circled those real numbers to be irrational.

Explanation:

Step1: Analyze $\frac{2}{5}$

$\frac{2}{5}=0.4$, which is a terminating decimal. Terminating decimals are rational.

Step2: Analyze $\sqrt{100}$

$\sqrt{100} = 10$, which is an integer. Integers are rational.

Step3: Analyze $\sqrt{50}$

$\sqrt{50}=5\sqrt{2}$. Since $\sqrt{2}$ is irrational (it cannot be written as a fraction of two integers), $5\sqrt{2}$ is also irrational.

Step4: Analyze $0.4545789$

It is a terminating decimal. Terminating decimals are rational.

Step5: Analyze $\pi$

$\pi$ is a non - repeating, non - terminating decimal. By definition, non - repeating, non - terminating decimals are irrational.

$\sqrt{50}=5\sqrt{2}$ and $\sqrt{2}$ is irrational (cannot be expressed as a fraction of two integers), so $\sqrt{50}$ is irrational. $\pi$ is a non - repeating, non - terminating decimal, so it is irrational. $\frac{2}{5}=0.4$ (terminating, rational), $\sqrt{100} = 10$ (integer, rational), $0.4545789$ (terminating, rational).

Answer:

Circle $\sqrt{50}$ and $\pi$.