Mathematics
11 Online
OpenStudy (anonymous):
Hey, please help:)
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OpenStudy (anonymous):
\[3 \sqrt[3]{24}\]
OpenStudy (klimenkov):
Hint:\[\sqrt[3]{24}=\sqrt[3]{8\cdot3}=\sqrt[3]8\cdot\sqrt[3]{3}\]
OpenStudy (anonymous):
Thank you!
OpenStudy (klimenkov):
Can you write the answer?
OpenStudy (anonymous):
\[6\sqrt[3]{3}\]
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OpenStudy (klimenkov):
Very nice.
OpenStudy (anonymous):
Could you help me with another question?
OpenStudy (anonymous):
\[3\sqrt{x+4}-2=13\]
OpenStudy (klimenkov):
What is the problem?
OpenStudy (klimenkov):
What cant you do?
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OpenStudy (klimenkov):
Solve for \(\sqrt{x+4}\).
OpenStudy (klimenkov):
Hey! Are you here?
OpenStudy (anonymous):
Yes, I am sorry
OpenStudy (anonymous):
couldn't I just do 4-2 giving me 2
so then I do x+2=13?
OpenStudy (anonymous):
x+2=13
-2 -2
x=11
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OpenStudy (anonymous):
idk
OpenStudy (klimenkov):
Can you solve \(3y-2=13\) ?
OpenStudy (anonymous):
y=5
OpenStudy (klimenkov):
Yes. Think if \(y=\sqrt{x+4}\).
OpenStudy (klimenkov):
If you make a substitution \(y=\sqrt{x+4}\), you will get \(\sqrt{x+4}=5\). Do you know what \(\sqrt{\phantom{a}}\) sign means?
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OpenStudy (anonymous):
square root
OpenStudy (klimenkov):
What does square root means?
OpenStudy (anonymous):
a number multiplied by itself?
OpenStudy (klimenkov):
Can you tell me what does \(\sqrt{16}\) mean?
OpenStudy (anonymous):
4?
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OpenStudy (klimenkov):
Yes. But Also -4 too. -4*(-4)=16.
So what can you say about \(\sqrt{x+4}=5\) ?
OpenStudy (anonymous):
x=1?
OpenStudy (anonymous):
I don't think I know
OpenStudy (klimenkov):
See the analogy. Try to think. Compute \(\sqrt{36}, \sqrt{25}, \sqrt{\frac14}\).
OpenStudy (anonymous):
alright. 6,5,2
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OpenStudy (klimenkov):
Check the last one.
OpenStudy (klimenkov):
\(\sqrt x\) is the inverse function for \(x^2\). \(\sqrt x\) is a number that squared must be \(x\). \((\sqrt x )^2=x\). Think about last one.
OpenStudy (anonymous):
I still think it's1
OpenStudy (klimenkov):
Compute \(\sqrt{\frac14}\).
OpenStudy (anonymous):
2
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OpenStudy (klimenkov):
\(2^2\neq\frac14\)
OpenStudy (klimenkov):
Try again.
OpenStudy (anonymous):
1/4
OpenStudy (klimenkov):
\(\left(\frac14\right)^2\neq\frac14\). Try again.
OpenStudy (anonymous):
So I have to square it?
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OpenStudy (klimenkov):
You have to find \(\sqrt{\frac14}\) using the definition I wrote above.
OpenStudy (anonymous):
.5
OpenStudy (anonymous):
.5*.5=1/4
OpenStudy (klimenkov):
Yes. Thats it. Now back to \(\sqrt{x+4}=5\). Can you solve it?
OpenStudy (anonymous):
Would I plug something in x?
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OpenStudy (klimenkov):
Ok. Can you solve this: \(\sqrt x = 2\) ?
OpenStudy (anonymous):
4
OpenStudy (klimenkov):
Yes. Thats it. Now back to \(\sqrt{x+4}=5\). Can you solve it?
OpenStudy (anonymous):
25?
OpenStudy (klimenkov):
\(\sqrt{25+4}\neq5\)
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OpenStudy (anonymous):
21
OpenStudy (klimenkov):
Bingo. You solved this by your own. Congratulations!
OpenStudy (anonymous):
It has to be that's why thought of 25 =5
OpenStudy (anonymous):
Thank you:)!!
OpenStudy (klimenkov):
You are welcome.