\(\sqrt{24+8\sqrt{5}}\)+\(\sqrt{9-4\sqrt{5}}\)
=\(\sqrt{2^2+2.2.\left(2\sqrt{5}\right)+\left(2\sqrt{5}\right)^2}\)+\(\sqrt{\left(\sqrt{5}\right)^2-2.2\sqrt{5}+2^2}\)
=\(\sqrt{\left(2+2\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5-2}\right)^2}\)
=2+2\(\sqrt{5}\)+\(\sqrt{5}\)-2=3\(\sqrt{5}\)
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√24+8√524+85+√9−4√59−45
=√22+2.2.(2√5)+(2√5)222+2.2.(25)+(25)2+√(√5)2−2.2√5+22(5)2−2.25+22
=√(2+2√5)2+√(√5−2)2(2+25)2+(5−2)2
=2+2√55+√55-2=3√5
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