Question

Let "x" = square root of 6 + the square root of 7. What two consecutive integers does "x" lie between? Can you please explain in words, how you got the answer?

Answer 1

(5, 6)

Explanation:

`x=√(6)+√(7)\approx2.45+2.65\approx 5.10\\\\\boxed{5<x<6}`

I evaluated the expression on my calculator.

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You can guess that the sum is nearly 2√6.5 = √26. This is between √5² and √6², so the root is likely between 5 and 6.