MHB How many integers in between \sqrt{19} and \sqrt{90}

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The integers between $\sqrt{19}$ and $\sqrt{90}$ are determined by identifying the smallest integer greater than $\sqrt{19}$ and the largest integer less than $\sqrt{90}$. Since $\sqrt{19}$ is approximately 4.36, the first integer greater than it is 5. Meanwhile, $\sqrt{90}$ is approximately 9.49, making the largest integer less than it equal to 9. Therefore, the integers between these two values are 5, 6, 7, 8, and 9. In total, there are five integers between $\sqrt{19}$ and $\sqrt{90}$.
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how many integers are between \sqrt{19} and \sqrt{90}
 
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prasadini said:
how many integers are between $\sqrt{19}$ and $\sqrt{90}$

You can use math tags "$$$$" or "$$" to encase your typeset equations.

Have you had a go at the problem?
 
Do you understand what this question is asking? 19 lies between 16 and 25 so the first integer larger than [math]\sqrt{19}[/math] is what? 90 lies between 81 and 100 so the last integer less than [math]\sqrt{90}[/math] is what?

How many integers lie between [math]\sqrt{19}[/math] and [math]\sqrt{90}[/math]?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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