Question

turn 10sqrt(10)+11sqrt(11) into the following exact answer:

sqrt( 2331+ 220sqrt(110))

Answer 1

\[10\sqrt{10}+11\sqrt{11} = \sqrt{2331+220\sqrt{110}}\]

Answer 2

\( 10\sqrt{10}+11\sqrt{11} = \sqrt{ (10+11)^2 +11(10+10)^2 \sqrt{(11\times 10)}}\)

Answer 3

\((10\sqrt{10}+11\sqrt{11})^2 = (10\sqrt{10})^2+(11\sqrt{11})^2+2\times 10\sqrt{10}\times 11\sqrt{11} \\= 10^2.10+11^2.11+ 2.10.11.\sqrt{11\times 10}\\
=(10^3+11^3)+(2\times10\times11)\sqrt{11\times 10} \\
=2331+220\sqrt{110 }\)

Answer 4

hmmm note that
220=11*(10+10) not 11*(10+10)^2

Answer 5

Your answer should be under a square root. Your answer = 3026.70... while the problem equals 68.105....

Answer 6

no no please read my answer
\((10\sqrt{10}+11\sqrt{11})^2 = 2331+220\sqrt{110 } \)
now take root for both sides
\(\sqrt{(10\sqrt{10}+11\sqrt{11})^2} = \sqrt{2331+220\sqrt{110 } }\\ 10\sqrt{10}+11\sqrt{11} = \sqrt{2331+220\sqrt{110 } } \)