jackoo
Hey, please help:)



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jackoo
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\[3 \sqrt[3]{24}\]

klimenkov
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Hint:\[\sqrt[3]{24}=\sqrt[3]{8\cdot3}=\sqrt[3]8\cdot\sqrt[3]{3}\]

jackoo
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Thank you!

klimenkov
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Can you write the answer?

jackoo
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\[6\sqrt[3]{3}\]

klimenkov
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Very nice.

jackoo
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Could you help me with another question?

jackoo
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\[3\sqrt{x+4}2=13\]

klimenkov
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What is the problem?

klimenkov
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What cant you do?

klimenkov
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Solve for \(\sqrt{x+4}\).

klimenkov
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Hey! Are you here?

jackoo
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Yes, I am sorry

jackoo
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couldn't I just do 42 giving me 2
so then I do x+2=13?

jackoo
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x+2=13
2 2
x=11

jackoo
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idk

klimenkov
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Can you solve \(3y2=13\) ?

jackoo
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y=5

klimenkov
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Yes. Think if \(y=\sqrt{x+4}\).

klimenkov
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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?

jackoo
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square root

klimenkov
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What does square root means?

jackoo
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a number multiplied by itself?

klimenkov
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Can you tell me what does \(\sqrt{16}\) mean?

jackoo
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4?

klimenkov
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Yes. But Also 4 too. 4*(4)=16.
So what can you say about \(\sqrt{x+4}=5\) ?

jackoo
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x=1?

jackoo
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I don't think I know

klimenkov
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See the analogy. Try to think. Compute \(\sqrt{36}, \sqrt{25}, \sqrt{\frac14}\).

jackoo
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alright. 6,5,2

klimenkov
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Check the last one.

klimenkov
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\(\sqrt x\) 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.

jackoo
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I still think it's1

klimenkov
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Compute \(\sqrt{\frac14}\).

jackoo
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2

klimenkov
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\(2^2\neq\frac14\)

klimenkov
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Try again.

jackoo
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1/4

klimenkov
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\(\left(\frac14\right)^2\neq\frac14\). Try again.

jackoo
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So I have to square it?

klimenkov
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You have to find \(\sqrt{\frac14}\) using the definition I wrote above.

jackoo
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.5

jackoo
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.5*.5=1/4

klimenkov
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Yes. Thats it. Now back to \(\sqrt{x+4}=5\). Can you solve it?

jackoo
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Would I plug something in x?

klimenkov
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Ok. Can you solve this: \(\sqrt x = 2\) ?

jackoo
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4

klimenkov
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Yes. Thats it. Now back to \(\sqrt{x+4}=5\). Can you solve it?

jackoo
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25?

klimenkov
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\(\sqrt{25+4}\neq5\)

jackoo
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21

klimenkov
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Bingo. You solved this by your own. Congratulations!

jackoo
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It has to be that's why thought of 25 =5

jackoo
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Thank you:)!!

klimenkov
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You are welcome.