geometry ... proofs
@mathmale
the highlitghed on the right is what i need help with... and on the left
Sounds as tho' there's an illustration that goes with this problem. Could you possibly share it?
NO
hehe
II, III, I, IV, V
this is an example by the way
i already know the answer to it
i just dont understand how people got it
did you get the picture
A picture of an algebra problem or of a geometry problem?
geometry, the link sends you to the triangle
this is algebra
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.
To answer this short set of questions properly, you need to know the precise definition of "rational." What is that def'n?
def of what ?
definition of the word "rational."
"A rational fraction is one in which ... what?"
for example 1/2 is rational it = 0.5
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.
okay
Look up "rational number" on the Internet for more examples.
sqrt(3) cannot be written as the ratio of two integers. That's why it's not rational. We say it's "irrational."
Regarding \[8^{\frac{ 1 }{ 3 }}\]
You could re-write that in "radical form," which would be \[\sqrt[3]{8}\]
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."
okay well i get all that but did i show enough work?
@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.
We are expected to explain why\[8^{\frac{ 1 }{ 3 }}\]
yes i know, to me i think i explained it pretty well, what do you think
is called the "cube root of 8." As before, I made use of the equality\[8^{\frac{ a }{ b }}=\sqrt[b]{8^a}\]
That is what you have to show. It's a test of your understanding of this concept.
Excuse me, y ou got Part A done just fine. What do you need to discuss or learn right now?
geometry @mathmale i will make new post
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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