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twenty three has no square root but it will be in between 4 squared and 5 squared but more towards the 5. also there is + and - square roots such as the two square roots of 9 are +3 and -3. - times - = + and + times + = +.
Two times the square root of three plus five times the square root of three plus four times the square root of three equals eleven times the square root of three.
The answer is easy to understand if we temporarily replace the phrase "square roots of 11"with the word "bean".Then the question becomes: "2 beans plus 3 beans", and we sense instinctively that the answermust be something close to 5 beans.In similar fashion . . .2 sqrt(11) + 3 sqrt(11) = 5 sqrt (11).
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No. The square roots of 2, 3 and 5, for a start, are not rational.