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

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lgbasalloteBest ResponseYou've already chosen the best response.0
what 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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
actually it is a 4th degree equation
 one year ago

CallistoBest 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'?
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
Oh.that's power 2, typo
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
apparently 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
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
I need to know how to work that out.....
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
cant seem to get it, i think it was a trick
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
............................ It... was ... a ... question ... asked ... when ... my friend applied for a summer job ...
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
really? doing what??
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
tutor  teaching high school students
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
hmm i wonder what answer they wanted
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
When 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 :(
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
multiplying by the conjugate give \(\frac{2}{\sqrt{5+\sqrt{21}}}\) think
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
any examples anywhere?
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
You 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
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
oops sqrt(2) on bottom
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
how did you get that identity?
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
lol great experience I want to prove that identity lol
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
First, \((\sqrt{a}  \sqrt{b})^2\) = 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?
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
ok i see that identity :)
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
that one is easy to prove
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
maybe because it is an actual identity, right? :p
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
Perfect square is perfect :)
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
Does that make sense? Apart from the latex fail...
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
very interesting i wouldn't have thought of that
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
I'm going to post the link to satellite73's post then. He doesn't even come to check..
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
Great work @Callisto :)
 one year ago

CallistoBest ResponseYou've already chosen the best response.4
And thank you for all your time!!!!
 one year ago
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