Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

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

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SEE EXPERT ANSWER

To see the expert answer you'll need to create a free account at Brainly

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
actually it is a 4th degree equation
\[(x^2-5)^2=21\]\[x^4-10x^2+25=21\]\[x^4-10x^2+4=0\]\[x^4-10x^2+4=0\]\[x^2=\frac{10\pm \sqrt{(-10)^6-4(4)}}{2}\]\[x^2=5\pm \sqrt{21}\]Sorry... are you sure that it is 'simplified'?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Oh.that's power 2, typo
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
I need to know how to work that out.....
cant seem to get it, i think it was a trick
............................ It... was ... a ... question ... asked ... when ... my friend applied for a summer job ...
really? doing what??
tutor - teaching high school students
hmm i wonder what answer they wanted
Same here...
When I was doing some exercises few days ago, I saw similar questions, but clearer, like this: express \(\sqrt{28-2\sqrt{147}}\) in the form of \(\sqrt{x}-\sqrt{y}\). I can still handle this. But that one, I failed :(
multiplying by the conjugate give \(\frac{2}{\sqrt{5+\sqrt{21}}}\) think
any examples anywhere?
example?!
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
oops sqrt(2) on bottom
how did you get that identity?
From experience...
lol great experience I want to prove that identity lol
First, \((\sqrt{a} - \sqrt{b})^2\) = a + b -2\sqrt{ab} For a>b \[\sqrt{5-\sqrt{21}} = \sqrt{5-2\sqrt{\frac{21}{4}}}\] Now, a+b = 5 => a=5-b ab = 21/4 (5-b)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?
ok i see that identity :)
that one is easy to prove
maybe because it is an actual identity, right? :p
Perfect square is perfect :)
Does that make sense? Apart from the latex fail...
very interesting i wouldn't have thought of that
I'm going to post the link to satellite73's post then. He doesn't even come to check..
Great work @Callisto :)
And thank you for all your time!!!!

Not the answer you are looking for?

Search for more explanations.

Ask your own question