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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 B : Method 1

| Comment 2 of 4 |

PART B

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V(7+7V7) vs 5

or, 7+7V7 vs 25

or, 7V7 vs 18

or, 343 vs 324 (squaring both sides)

since, 343 > 324, it follows that:

V(7+7V7) is greater than 5

This is corroborated by calculator as:

V(7+7V7) ~= 5.051758028

Edited on June 3, 2022, 8:06 am

Posted by K Sengupta on 2022-06-03 07:14:58

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