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Number Theory Level pending

Solve without using the calculator to indicate which quantity is greater:

Quantity A A : ( 1 , 111 , 111 ) 2 3 \sqrt[3]{(1,111,111)^2}

Quantity B B : 9 , 999 9,999

B A The realtionship can not be determined The two quantities are equal

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Zee Ell
Sep 12, 2016

A = 1 , 111 , 11 1 2 3 > 1 , 000 , 00 0 2 3 = 10000 > 9999 = B A = \sqrt [3] {1,111,111^2} > \sqrt [3] {1,000,000^2} = 10000 > 9999 = B

Hence, A > B \text {Hence, } \boxed {A > B}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice, brief and elegant solution.

Hana Wehbi - 4 years, 9 months ago

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