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anonymous

  • one year ago

turn 10sqrt(10)+11sqrt(11) into the following exact answer: sqrt( 2331+ 220sqrt(110))

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  1. anonymous
    • one year ago
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    \[10\sqrt{10}+11\sqrt{11} = \sqrt{2331+220\sqrt{110}}\]

  2. anonymous
    • one year ago
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    \( 10\sqrt{10}+11\sqrt{11} = \sqrt{ (10+11)^2 +11(10+10)^2 \sqrt{(11\times 10)}}\)

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

  4. anonymous
    • one year ago
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    hmmm note that 220=11*(10+10) not 11*(10+10)^2

  5. anonymous
    • one year ago
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    Your answer should be under a square root. Your answer = 3026.70... while the problem equals 68.105....

  6. anonymous
    • one year ago
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    no no please read my answer \((10\sqrt{10}+11\sqrt{11})^2 = 2331+220\sqrt{110 } \) now take root for both sides \(\sqrt{(10\sqrt{10}+11\sqrt{11})^2} = \sqrt{2331+220\sqrt{110 } }\\ 10\sqrt{10}+11\sqrt{11} = \sqrt{2331+220\sqrt{110 } } \)

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spraguer (Moderator)
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