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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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