Question

√5 = ?
betweens
1&2 2&3 3&4 4&5 5&6 6&7 7&8 8&9 9&10
0 1 2 3 4 5 6 7 8 9 10 11

Explanation:

Step1: Recall square of integers

We know that \(2^2 = 4\) and \(3^2=9\).

Step2: Compare with 5

Since \(4<5<9\), taking square roots (which is a monotonic function for non - negative numbers), we get \(\sqrt{4}<\sqrt{5}<\sqrt{9}\), that is \(2 < \sqrt{5}<3\). So \(\sqrt{5}\) is between 2 and 3.

Step3: Find the decimal approximation (optional for the range)

Calculating the decimal value of \(\sqrt{5}\approx2.236\), which is still between 2 and 3.

Answer:

The value of \(\sqrt{5}\) is between 2 and 3 (in the "2 & 3" interval). And the decimal approximation of \(\sqrt{5}\) is approximately \(2.24\) (if a numerical answer is needed, \(\sqrt{5}\approx2.24\)).