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Callisto
 3 years ago
Tutor question #3
Simplify:
\[\sqrt{5\sqrt{21}}\]
(conditions: pen, paper, no calculator, done in 2 minutes)
*
Callisto
 3 years ago
Tutor question #3 Simplify: \[\sqrt{5\sqrt{21}}\] (conditions: pen, paper, no calculator, done in 2 minutes) *

This Question is Closed

anonymous
 3 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

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

Callisto
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.4Oh.that's power 2, typo

anonymous
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.4I need to know how to work that out.....

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

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

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

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

Callisto
 3 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 :(

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

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

myininaya
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0oops sqrt(2) on bottom

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

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

Callisto
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0ok i see that identity :)

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

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

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

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

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

Callisto
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0Great work @Callisto :)

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