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Question

What is the square root of 2 plus the square root of 3?

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Solution

2+3 is not readily simplifiable.
You can calculate an approximate value as:
2+31.414213562+1.732050808=3.146264370
Funnily enough, I was intrigued the other day to find the simplest polynomial with integer coefficients of which 2+3 is a root.
The answer is : x410x2+1=0
which has roots:2+3
23
2+3
23
and x410x2+1 has factors:(x23)
(x2+3)
(x+23)
(x+2+3)

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