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Simplify \(\sqrt{5 + \sqrt{24}}\)

 Jun 12, 2020
 #1
avatar+80 
0

3.14626436994

sqrt of 24 = 4.89897948557 

add 5 = 9.89897948557

The find the sqrt of 9.89897948557 = 3.14626436994

 

I am not sure if this is right...

 Jun 12, 2020
edited by Sarvajit  Jun 12, 2020
 #2
avatar+684 
0

Well I got sqrt(5+2sqrt(6)) and sqrt(6) is about 2.44948974 and 2.44948974*2=4.89897948 also 4.89897948+5=9.89897948 then we solve sqrt(9.89897948) is about 3.14626437 so I agree that it is correct 

jimkey17  Jun 12, 2020
 #3
avatar+649 
+1

hmm i think guest wanted it to be simplified exactly (like in simpler terms of radicals)...

 

here's my try at this problem:

 

\(\sqrt{5+\sqrt{24}}=\sqrt{5+2\sqrt{6}}\)

 

so we can express \(\sqrt{5+2\sqrt{6}}\)  in the form of \((a+b)^2\)

 

so we know that \(a^2+b^2=5 \text{ and } 2ab=\sqrt{6}\), so it's really easy to figure out that \(a=\sqrt{2} \text{ and } b=\sqrt{3}\)

 

so this would become \(\sqrt{(\sqrt{2}+\sqrt{3})^2}\)

 

which means the equation is really just equal to \(\boxed{\sqrt{2}+\sqrt{3}}\)

 

i hope this helped you! :)

 Jun 12, 2020

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