Estimating Square Roots
Ever wondered how to estimate the value of a square root that isn't a perfect square? It's actually pretty simple!
To estimate a square root to the nearest integer, first identify the perfect squares that come before and after your number. For example, with √8, we know that 4 and 9 are perfect squares (2² and 3²), so 8 is between them. This means √8 is between 2 and 3.
To make the best estimate, see which perfect square is closer to your number. Since 8 is closer to 9 than to 4, we estimate √8 ≈ 3. For √83, we'd compare it to √81 (which equals 9) and √100 (which equals 10). Since 83 is closer to 81, our best estimate is 9.
Quick Tip: Draw a number line with the perfect squares marked if you're having trouble visualizing where your number falls. This makes it easier to see which whole number estimate makes the most sense!
