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# Find the set of all rea numbers x so that Express your answer in interval notation

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Find the set of all rea numbers x so that $$\lfloor x^2 \rfloor = 3$$ Express your answer in interval notation

May 26, 2021

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Floor basically means... rounding down to the nearest number.

Thus, we should set $$3 \leq x^2 < 4$$

Similarly, we can also set $$-3 \leq x^2 < -4$$

Taking the square root gives... $$\sqrt{3} \leq x < \sqrt{4}$$ and $$-\sqrt{3} \leq x < -\sqrt{4}$$.

Thus entering in integer notation $$(-\sqrt{4}, -\sqrt{3}] \cup [\sqrt{3}, \sqrt{4})$$. (square bracket = include end, round bracket = don't include end, U = union (include both in solution).

May 26, 2021