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Mathematics 6 Online
OpenStudy (itrymath):

geometry ... proofs

OpenStudy (itrymath):

@mathmale

OpenStudy (itrymath):

the highlitghed on the right is what i need help with... and on the left

OpenStudy (mathmale):

Sounds as tho' there's an illustration that goes with this problem. Could you possibly share it?

OpenStudy (itrymath):

NO

OpenStudy (itrymath):

hehe

OpenStudy (itrymath):

II, III, I, IV, V

OpenStudy (itrymath):

this is an example by the way

OpenStudy (itrymath):

i already know the answer to it

OpenStudy (itrymath):

i just dont understand how people got it

OpenStudy (itrymath):

did you get the picture

OpenStudy (mathmale):

A picture of an algebra problem or of a geometry problem?

OpenStudy (itrymath):

geometry, the link sends you to the triangle

OpenStudy (itrymath):

OpenStudy (itrymath):

this is algebra

OpenStudy (mathmale):

If one dimension is 3 and the other is sqrt(3), the area is 3sqrt(3). Because sqrt(3) is irrational, the area 3sqrt(3) is also irrational. 3*4 would be rational. 3*2.5 would be rational. But 3sqrt(3) is irrational.

OpenStudy (mathmale):

To answer this short set of questions properly, you need to know the precise definition of "rational." What is that def'n?

OpenStudy (itrymath):

def of what ?

OpenStudy (mathmale):

definition of the word "rational."

OpenStudy (mathmale):

"A rational fraction is one in which ... what?"

OpenStudy (itrymath):

for example 1/2 is rational it = 0.5

OpenStudy (mathmale):

1/2 is rational, but not because it equals 0.5. 1/2 is rational because it's the ratio of two integers. 1 is an integer and 2 is also.

OpenStudy (itrymath):

okay

OpenStudy (mathmale):

Look up "rational number" on the Internet for more examples.

OpenStudy (mathmale):

sqrt(3) cannot be written as the ratio of two integers. That's why it's not rational. We say it's "irrational."

OpenStudy (mathmale):

Regarding \[8^{\frac{ 1 }{ 3 }}\]

OpenStudy (mathmale):

You could re-write that in "radical form," which would be \[\sqrt[3]{8}\]

OpenStudy (mathmale):

Notice that this is a radical, and the "index of the root" is 3. That's why 8^(1/3) is called the "cube root of 8."

OpenStudy (itrymath):

okay well i get all that but did i show enough work?

OpenStudy (itrymath):

@mathmale

OpenStudy (mathmale):

It's not a matter of "showing enough work." The "work" has to be correct. I would not say that the explanation I gave you is the only possible one. However, I reviewed a concept that you need to know: that exponential functions can be expressed as radicals and radical functions can be expressed as exponential functions.

OpenStudy (mathmale):

We are expected to explain why\[8^{\frac{ 1 }{ 3 }}\]

OpenStudy (itrymath):

yes i know, to me i think i explained it pretty well, what do you think

OpenStudy (mathmale):

is called the "cube root of 8." As before, I made use of the equality\[8^{\frac{ a }{ b }}=\sqrt[b]{8^a}\]

OpenStudy (mathmale):

That is what you have to show. It's a test of your understanding of this concept.

OpenStudy (mathmale):

Excuse me, y ou got Part A done just fine. What do you need to discuss or learn right now?

OpenStudy (itrymath):

geometry @mathmale i will make new post

OpenStudy (mathmale):

In the first and only geometry problem you've shared with me, your job was to arrange the 5 steps in the proof in correct order. I overlooked that at first.

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