Root of root!

Algebra Level 2

A = 12 + 12 + 12 + 12 + 12 + 6 + 6 + 6 + 6 B = 15 + 11 \begin{aligned} A &=& \sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12 + \sqrt{12}}}}} + \sqrt{6+\sqrt{6+\sqrt{6 +\sqrt6}}} \\ B &=& \sqrt{15} + \sqrt{11} \end{aligned}

Which of these numbers is bigger?

There is inadequate information They are both equal A B

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1 solution

Brian Blass
Nov 6, 2015

A < 7

because the infinite square roots of 12 and 6 are 4 and 3 respectively.

The square roots in the problem terminate so A will be slightly less than 7.

15 > 3.8 11 > 3.1 \sqrt { 15 } >\quad 3.8\\ \sqrt { 11 } >\quad 3.1

so B > 7.1

B > A

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