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# help

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Simplify $$\sqrt{5 + \sqrt{24}}$$

Jun 12, 2020

#1
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3.14626436994

sqrt of 24 = 4.89897948557

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
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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
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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