Question

Which 3 of the following numbers are irrational?
PLEASE ONLY ANSWER IF YOU KNOW THE ANSWER.

$13 + \sqrt{25}$
$17\pi$
$.21475467...$
$\sqrt{ \frac{9 }{16} }$
$- \frac{4}{5} + \sqrt{ \frac{6}{9} }$


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Answer 1

P(red,not green)with replacement

Answer 2

Answer:

The irrational numbers from the given options are :-

• $17\pi$
• $0.21475467.....$
• $-\frac{4}{5} + \sqrt{\frac{6}{9} }$

Step-by-step explanation:

Analyse each option carefully.

1) $13 + \sqrt{25}$ is a rational number because :-

• $\sqrt{25} = 5$
• $13 + \sqrt{25} = 13 + 5 = 18$ , which is a rational number.

2) $17\pi$ is irrational because :-

• Value of π has a non-terminating & non-recurring decimal value. So it is irrational number.
• If π is irrational , then 17π is also irrational because product of any number and an irrational number is always irrational.

3) $0.21475467....$ is irrational because :-

• It is a non-terminating & non-recurring decimal.

• Any non terminating & non-recurring decimal is an irrational number.

4) $\sqrt{\frac{9}{16} }$ is rational because :-

• $\sqrt{\frac{9}{16} } = \frac{\sqrt{9} }{\sqrt{16} } = \frac{3}{4}$.
• $\frac{3}{4}$ is a rational number.

5) $-\frac{4}{5} + \sqrt{\frac{6}{9} }$ is irrational because :-

• $\sqrt{\frac{6}{9} } = \frac{\sqrt{6} }{\sqrt{9} } = \frac{\sqrt{6} }{3}$ , which is irrational.
• If $\frac{\sqrt{6} }{3}$ is irrational , then $-\frac{4}{5} + \sqrt{\frac{6}{9} }$ is also irrational because sum of any number and an irrational number is always an irrational number.