Question

1. compare the following number using <, >, or =. \\(\sqrt{5}\\) \\(\boldsymbol{7}\\) 2.25645324...

Explanation:

Step1: Calculate the approximate value of $\sqrt{5}$

We know that $2^2 = 4$ and $3^2=9$, so $\sqrt{5}$ is between 2 and 3. Using a calculator, $\sqrt{5}\approx2.23607$.

Step2: Compare $\sqrt{5}$ and $2.25645324...$

Now we compare the approximate value of $\sqrt{5}$ (which is approximately $2.23607$) with $2.25645324...$. Since $2.23607< 2.25645324...$, we can conclude that $\sqrt{5}<2.25645324...$.

Answer:

$\sqrt{5}<2.25645324...$