A community for students.
Here's the question you clicked on:
 0 viewing
Jonask
 3 years ago
which one is larger
Jonask
 3 years ago
which one is larger

This Question is Closed

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt[3]{60}\] \[2+\sqrt[3]{7}\]no machines allowed

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0\[60=(\frac{ 7+8 }{ 2 })10\]

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt[3]{60}= \sqrt[3]{5}(\sqrt[3]{7+8})\]

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0almost simlar now to\[\sqrt[3]{8}+\sqrt[3]{7}\] HALT

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0is comparing 60 with \[(2+\sqrt[3]{7})^3\]the same idea(tautology)

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0i think we have to use inequalities \[(2+\sqrt[3]{7})^3=8+3(4)\sqrt[3]{7}+3(2)(\sqrt[3]{7})^2+7\]

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt[3]{1}<\sqrt[3]{7}<\sqrt[3]{8}\]

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.1Interesting question!

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ x+y+z }{ 3 } \leq \sqrt[3]{xyz}\] useful ineq

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.1Try to do like this. How to evaluate \(\sqrt[3]{7}\). \(1<{7}<8 \Rightarrow 1<\sqrt[3]{7}<2\). As 7 is closer to 8 than to 1, I hope \(\sqrt[3]{7}\) is closer to 2. Lets put \(\sqrt[3]{7}=2+\alpha\). Then \(7=8+12\alpha+6\alpha^2+\alpha^3\). Since \(\alpha <1\) we can neglect \(\alpha^2 ,\alpha^3\). So, \(\alpha=\frac1{12}\). So the approximation for \(\sqrt[3]{7}\) is \(2\frac1{12}=\frac{23}{12}\). Do this once again, because it is not a good accuracy for this problem.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.