Estimation Math Example 2

Solution

1. 1
   Identify perfect squares near 52: $7^2 = 49$ and $8^2 = 64$. So $7 < \sqrt{52} < 8$.
2. 2
   52 is close to 49 (only 3 away), but far from 64 (12 away). Try $7.2$: $7.2^2 = 51.84$. Try $7.3$: $7.3^2 = 53.29$.
3. 3
   Since $51.84 < 52 < 53.29$ and 52 is closer to 51.84, $\sqrt{52} \approx 7.2$.