Which is rational and irrational numbers.

Question

cookie_2046 · Answer

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mathstudent55 · Answer

A rational number is a number that can be written as a fraction of integers.
All integers are rational. Any decimal number that ends or that repeats is also rational.

An irrational number is a number that cannot be written as a fraction of integers.
All non-terminating, non-repeating decimals are irrational.

mathstudent55 · Answer

What is $\sqrt 4$ equal to?

cookie_2046 · Answer

2

mathstudent55 · Answer

Correct.
2 is an integer, so it is rational. 2 can be written as 2/1, a fraction of integers, so once again, 2 is rational.

mathstudent55 · Answer

What about 2/3?

cookie_2046 · Answer

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mathstudent55 · Answer

No. 
2/3 has no square root in it.
2 is an integer, and 3 is an integer. 
A fraction of integers is rational.

mathstudent55 · Answer

Next is $\sqrt 8$.
If you find the value of $ \sqrt 8$ using a calculator, you will find a never ending decimal number that does not repeat. Look above to see if it's rational or irrational.

mathstudent55 · Answer

Then you have $\dfrac{\pi}{2}$ and $\pi$.
$\pi$ is a famous never-ending, never-repeating decimal number.

mathstudent55 · Answer

For $\sqrt {90}$, use your calculator. It is a decimal number. Does it repeat?

cookie_2046 · Answer

$$\sqrt{8} $$ That is irrational

mathstudent55 · Answer

Finally, you have 1/4.
This is a fraction of integers, like 2/3.

mathstudent55 · Answer

Correct. $\sqrt 8$ is irrational.

cookie_2046 · Answer

$$\left| \frac{ 1 }{ 4 } \right|$$ thats rational i think

mathstudent55 · Answer

Yes. A fraction of integers is rational.