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# The square root of 2x is greater than 3 and less than 4. How many integer values of x satisfy this condition?

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The square root of 2x is greater than 3 and less than 4. How many integer values of x satisfy this condition?

Nov 13, 2021

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$$3\lt\sqrt{2x}\lt4\\~\\ 3^2\lt(\sqrt{2x}\ )^2\lt4^2\\~\\ 9\lt2x\lt16\\~\\ \frac92\lt\frac{2x}{2}\lt\frac{16}{2}\\~\\ 4.5 \lt x \lt 8$$

The integers between 4.5 and 8 exclusively are:

5, 6, 7

So there are 3 different integer values of  x  that satisfy the condition.

Nov 13, 2021