Value Comparison: Identifying the Maximum Among Given Numbers

Memorize common perfect squares: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25. So $\sqrt{25} = 5$ because 5² = 25!

Start with what you know! If you remember $\sqrt{9} = 3$, you can work up: 4² = 16, so $\sqrt{16} = 4$, then 5² = 25, so $\sqrt{25} = 5$.

The numbers under the radical don't have a linear relationship to the square root values. For example, 25 is much bigger than 16, but $\sqrt{25} = 5$ is only slightly bigger than $\sqrt{16} = 4$.

Yes! Notice the pattern: 1, 4, 9, 16, 25, 36, 49... Each perfect square increases by the next odd number: +3, +5, +7, +9, +11, +13. This can help you remember them in order!

You'd need to estimate or use a calculator. For example, $\sqrt{20}$ is between $\sqrt{16} = 4$ and $\sqrt{25} = 5$, so approximately 4.5.