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Nested radical (Posted on 2022-06-03)

Without a calculator: Which is greater √(5+5√5) or 4?

Without a calculator: Which is greater √(7+7√7) or 5?

No Solution Yet Submitted by Jer

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Puzzle Solution Part A : Method 1

| Comment 1 of 4

PART A

------------

V(5+5*V5) vs 4

or, 5 +5*V5 vs 4^2= 16

or, 5V5 vs 11

or, (5V5)^2 vs 11^2

or, 125 vs 121

Since 125 > 121, it follows that:

V(5+5V5) >4

This is corroborated by calculator, as:

V(5+5V5) ~= 4.022479 > 4

Posted by K Sengupta on 2022-06-03 07:09:35

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