help

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...

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! :)