TwiztTiez
  • TwiztTiez
Which number is irrational. A. 0.14 sorry for not knowing math terms and such but there's a bar above the "14" B. 1/3 C. pi 4 D. pi 6
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
TwiztTiez
  • TwiztTiez
@mathmate
mathmate
  • mathmate
Do you know what is an irrational number?
TwiztTiez
  • TwiztTiez
Isn't it a number that can be put in decimal form or percentage form?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

TwiztTiez
  • TwiztTiez
can't*
TwiztTiez
  • TwiztTiez
Oops
mathmate
  • mathmate
In mathematics, many of the questions can be answered correctly if we know the definition of the terms. If we do not know what the terms mean, the question will appear difficult. So the first step is to understand the meaning of the terms. From wiki: "a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero." " an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals."
mathmate
  • mathmate
Are the terms clear to you now?
TwiztTiez
  • TwiztTiez
Somewhat
mathmate
  • mathmate
For example: (not the same as the first option) 0.14 = 14/100 =7/50, so it can be expressed as a fraction. is it rational?
TwiztTiez
  • TwiztTiez
Yes
TwiztTiez
  • TwiztTiez
Right?
mathmate
  • mathmate
Good!
TwiztTiez
  • TwiztTiez
Okay
TwiztTiez
  • TwiztTiez
So a number that can become a Fraction or a decimal correct?
mathmate
  • mathmate
Now the number 0.13333333333... is called a repeting decimal. It can be converted to a fraction as 2/15
mathmate
  • mathmate
All repeting decimals can be converted to a fraction.
TwiztTiez
  • TwiztTiez
Oooookay
TwiztTiez
  • TwiztTiez
So we're looking for a number that can't be turned into a fraction right?
mathmate
  • mathmate
Right! If you need further help, let me know.
TwiztTiez
  • TwiztTiez
Oops
TwiztTiez
  • TwiztTiez
Option C and D were supposed to be 4 to the fourth and 6 to the fourth
mathmate
  • mathmate
I knew there was a typo! So are you all good now?
TwiztTiez
  • TwiztTiez
Yes I think it would be D I don't know if I'm correct though
TwiztTiez
  • TwiztTiez
@mathmate
mathmate
  • mathmate
To avoid communication errors, please give me the answer and not the letter.
TwiztTiez
  • TwiztTiez
Oh okay sorry ^-^
TwiztTiez
  • TwiztTiez
6 to the fourth
TwiztTiez
  • TwiztTiez
You said that repeating decimals can be turned into fractions and A and B are both repeating
TwiztTiez
  • TwiztTiez
And 4 to the fourth is 2
TwiztTiez
  • TwiztTiez
You there?
TwiztTiez
  • TwiztTiez
@mathmate
TwiztTiez
  • TwiztTiez
Hello?
TwiztTiez
  • TwiztTiez
@campbell_st
campbell_st
  • campbell_st
well pi is irrational.... so dividing it by anything results in an irrational number.
TwiztTiez
  • TwiztTiez
Oh sorry
TwiztTiez
  • TwiztTiez
I mistyped earlier
TwiztTiez
  • TwiztTiez
4 and 6 are supposed to be put to the fourth
campbell_st
  • campbell_st
that's ok... I think there are 2 irrational numbers in your answer choices... they both involve pi...
TwiztTiez
  • TwiztTiez
Yeah as I said C and D aren't supposed to have Pi
TwiztTiez
  • TwiztTiez
They're supposed to be put to the fourth
campbell_st
  • campbell_st
can you use the draw function to write them
TwiztTiez
  • TwiztTiez
\[\sqrt{4} \sqrt{6}\]
campbell_st
  • campbell_st
I'll let @mathmate continue to answer this
mathmate
  • mathmate
@TwiztTiez Remember that all integers are rational, because 5 is the same as 5/1, so it can be represented by a fraction. So the 4 choices are: 1.44444444..... (or 1.4 with a rep. dec. bar) 1/3 4^6 6^6 ? That's why I prefer dealing with the actual numbers, not the choice letters.
mathmate
  • mathmate
or rather 1.44444444..... (or 1.4 with a rep. dec. bar) 1/3 4^6 \(\sqrt4 \sqrt6\) which is the same as \(\sqrt{24}\)
mathmate
  • mathmate
Which one of these can you NOT represent by a fraction?
TwiztTiez
  • TwiztTiez
I didn't mean for it to look like they were supposed to multiplied sorry
mathmate
  • mathmate
That's ok, the multiplication is understood. I just used the law of exponents to simplify it.
TwiztTiez
  • TwiztTiez
Well \[\sqrt{4} =2\]
mathmate
  • mathmate
For your information 1.4444444... equals 13/9.
mathmate
  • mathmate
Very good start, continue! So \(\sqrt{4}\sqrt6=2\sqrt{6}\) can you go further?
TwiztTiez
  • TwiztTiez
Yup yup
mathmate
  • mathmate
I'll put it this way, can you represent \(\sqrt6\) by a fraction?
TwiztTiez
  • TwiztTiez
4.8989794
mathmate
  • mathmate
...mathematically exactly?
TwiztTiez
  • TwiztTiez
\[2\sqrt{6}=4.8989794...\]
mathmate
  • mathmate
2.449489742783178.... and this is not exact.
mathmate
  • mathmate
4.898979485566356... and this is not exact.
TwiztTiez
  • TwiztTiez
Well how can I make it exact? Is there a way or am I just being oblivious?
TwiztTiez
  • TwiztTiez
And I don't mean that rudely
TwiztTiez
  • TwiztTiez
Sorry if it came off that way
mathmate
  • mathmate
Well, there is no way to represent a square root in decimal form unless it is a perfect square. What does that mean (in the context of this question)?
mathmate
  • mathmate
4.89897948556635619639456814941178278393189496131334025686539... and this is still not exact!
TwiztTiez
  • TwiztTiez
Oh okay so
TwiztTiez
  • TwiztTiez
\[\sqrt{4}=2\]
TwiztTiez
  • TwiztTiez
That's exact right?
mathmate
  • mathmate
yes, sqrt(4) is rational.
TwiztTiez
  • TwiztTiez
Okay I get it
mathmate
  • mathmate
but is sqrt(6)?
mathmate
  • mathmate
It can be proved mathematically that square root of a number (such as 2, 3, 5,6,...) is not rational unless the number is a perfect square (1,4,9,16,25....)
TwiztTiez
  • TwiztTiez
2.44948974278
TwiztTiez
  • TwiztTiez
So no I don't think so
mathmate
  • mathmate
You can read more about it (and it is interesting reading for general information) at, for example, Wiki: http://en.wikipedia.org/wiki/Irrational_number or http://www.purplemath.com/modules/numtypes.htm
TwiztTiez
  • TwiztTiez
Thanks!
mathmate
  • mathmate
Correct, since sqrt(6) is not rational, so 2sqrt(6) is also not rational. Does that clear things up a little?
TwiztTiez
  • TwiztTiez
It does thanks for the help!
mathmate
  • mathmate
Good, you're welcome! :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.