A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
Tutor question #3
Simplify:
\[\sqrt{5\sqrt{21}}\]
(conditions: pen, paper, no calculator, done in 2 minutes)
*
 2 years ago
Tutor question #3 Simplify: \[\sqrt{5\sqrt{21}}\] (conditions: pen, paper, no calculator, done in 2 minutes) *

This Question is Closed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0what if x = \(\sqrt{5\sqrt{21}}\) then \(x^2 = 5  \sqrt{21}\) \[x^2  5 = \sqrt{21}\] \[(x^2  5)^2 = 21\] oh goodness quadratic o.O

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0actually it is a 4th degree equation

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4\[(x^25)^2=21\]\[x^410x^2+25=21\]\[x^410x^2+4=0\]\[x^410x^2+4=0\]\[x^2=\frac{10\pm \sqrt{(10)^64(4)}}{2}\]\[x^2=5\pm \sqrt{21}\]Sorry... are you sure that it is 'simplified'?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4Oh.that's power 2, typo

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0apparently it is also \[\sqrt{\frac{7}{2}}\sqrt{\frac{3}{2}}\] i remember seeing something like this before but i am not sure i remember how to go from one to the other

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4I need to know how to work that out.....

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0cant seem to get it, i think it was a trick

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4............................ It... was ... a ... question ... asked ... when ... my friend applied for a summer job ...

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0really? doing what??

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4tutor  teaching high school students

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0hmm i wonder what answer they wanted

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4When I was doing some exercises few days ago, I saw similar questions, but clearer, like this: express \(\sqrt{282\sqrt{147}}\) in the form of \(\sqrt{x}\sqrt{y}\). I can still handle this. But that one, I failed :(

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0multiplying by the conjugate give \(\frac{2}{\sqrt{5+\sqrt{21}}}\) think

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0any examples anywhere?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0You want to show \[\sqrt{5\sqrt{21}} \text{ equals } \frac{\sqrt{7}\sqrt{3}}{2} ?\] was just wondering if you have an example for writing that one thing in that other form

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0oops sqrt(2) on bottom

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0how did you get that identity?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0lol great experience I want to prove that identity lol

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4First, \((\sqrt{a}  \sqrt{b})^2\) = a + b 2\sqrt{ab} For a>b \[\sqrt{5\sqrt{21}} = \sqrt{52\sqrt{\frac{21}{4}}}\] Now, a+b = 5 => a=5b ab = 21/4 (5b)b = 21/4 4b^2 + 20b  21 =0 b=1.5 or b =3.5 (rejected) a = 5  1.5 = 3.5 So, it is \(\sqrt{\frac{7}{2}}\sqrt{\frac{3}{2}}\) Does that make sense?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0ok i see that identity :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0that one is easy to prove

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0maybe because it is an actual identity, right? :p

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4Perfect square is perfect :)

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4Does that make sense? Apart from the latex fail...

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0very interesting i wouldn't have thought of that

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4I'm going to post the link to satellite73's post then. He doesn't even come to check..

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.0Great work @Callisto :)

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.4And thank you for all your time!!!!
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.