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

- Callisto

- katieb

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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- lgbasallote

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

- anonymous

actually it is a 4th degree equation

- Callisto

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- Callisto

Oh.that's power 2, typo

- anonymous

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

- Callisto

I need to know how to work that out.....

- anonymous

cant seem to get it, i think it was a trick

- Callisto

............................
It... was ... a ... question ... asked ... when ... my friend applied for a summer job ...

- anonymous

really? doing what??

- Callisto

tutor - teaching high school students

- anonymous

hmm i wonder what answer they wanted

- Callisto

Same here...

- Callisto

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 :(

- anonymous

multiplying by the conjugate give \(\frac{2}{\sqrt{5+\sqrt{21}}}\) think

- myininaya

any examples anywhere?

- Callisto

example?!

- myininaya

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

- myininaya

oops sqrt(2) on bottom

- myininaya

how did you get that identity?

- Callisto

From experience...

- myininaya

lol great experience
I want to prove that identity lol

- Callisto

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?

- myininaya

ok i see that identity :)

- myininaya

that one is easy to prove

- myininaya

maybe because it is an actual identity, right? :p

- Callisto

Perfect square is perfect :)

- Callisto

Does that make sense?
Apart from the latex fail...

- myininaya

very interesting
i wouldn't have thought of that

- Callisto

I'm going to post the link to satellite73's post then. He doesn't even come to check..

- myininaya

Great work @Callisto :)

- Callisto

And thank you for all your time!!!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.