perplexus.info :: Just Math : Which is Greater?

Which is Greater? (Posted on 2023-11-24)

Which is greater: √2^√7 or √3^√3?

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See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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possible solution

Comment 1 of 1

Square both sides

2^√7 or 3^√3

Take the base-10 logarithm of both sides.

√7log2 or √3log3

Then use (well?) known estimates rounding up on the left and down on the right

2.7*0.302 or 1.732*0.477

0.8154 or 0.8262

√2^√7 < √3^√3

Posted by Jer on 2023-11-24 15:21:14

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