Question

square roots
√7 = ?
betweens
1&2 2&3 3&4 4&5 5&6 6&7 7&8 8&9 9&10

Explanation:

Step1: Recall square values

We know that $2^2 = 4$ and $3^2 = 9$.

Step2: Compare with 7

Since $4<7<9$, taking square roots (which is a monotonic function for non - negative numbers), we have $\sqrt{4}<\sqrt{7}<\sqrt{9}$, that is $2 < \sqrt{7}<3$. So $\sqrt{7}$ is between 2 and 3.

Answer:

The value of $\sqrt{7}$ is between 2 and 3 (approximately 2.6458).