Do all look irrational?

Number Theory Level 3

Which of these numbers is/are rational?

$1. \ \sqrt{\pi^2}$
$2. \ \sqrt[3]{0.8}$
$3. \ \sqrt[4]{0.00016}$
$4. \ \sqrt[3]{-1}$

All 2 and 3 2 and 4 Only 4 None Only 3

1 solution

Kay Xspre
Feb 8, 2016

$|π|$ is irrational. The other two may be reduced to $\frac{2}{\sqrt[3]{10}}$ and $\frac{2}{10\sqrt[4]{10}}$ , which is also irrational. Only $\sqrt[3]{-1} = -1$ is rational

What about the other 2 values of (-1)^1/3?

Kushagra Sahni - 5 years, 4 months ago

I think you make reason , it should be clarified, althought I answered good this question so it's the same for me.

Guillermo Templado - 5 years, 3 months ago

Not real number, nor does the other two choices of (2) and (4). This question only wants us to evaluate the value in real number.

Kay Xspre - 5 years, 4 months ago

What's $|\pi|$ ??? No sense of putting mod on $\pi$ as it is already positive.

Rishabh Jain - 5 years, 4 months ago

Bhaiya square root yields positive values so that's why mod...

Department 8 - 5 years, 4 months ago

What's the need to apply mod on something that's already positive!! $(\pi=3.1415..>0$ )

Rishabh Jain - 5 years, 4 months ago

@Rishabh Jain – Hmmm..... That's strange may be @Kay Xspre would help

Department 8 - 5 years, 4 months ago

@Department 8 – One important question( it's irrelevant )..Who do you support among Lesnar, Reigns and Ambrose in the Triple Threat match for Wrestlemania against HHH..

Rishabh Jain - 5 years, 4 months ago

@Rishabh Jain – Lesnar the beast

Department 8 - 5 years, 4 months ago

@Rishabh Jain – I put absolute value to satisfy the $\sqrt{x^2} = |x|$ , as a number of people is likely to assume $\sqrt{x^2} = \pm x$

Kay Xspre - 5 years, 4 months ago

Do all look irrational?

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