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Square roots
Estimate positive and negative square roots

You can estimate the square roots of numbers that are not perfect squares.

 Estimating Square Roots To estimate the square roots of r, find perfect squares on each side of r. Use these to estimate.

 a. Estimate $\sqrt{38}$to the nearest whole number b. Estimate $\sqrt{21.6}$to the nearest whole number Find a perfect square a little less than 38 and one a little more than 38. $\sqrt{36}<\sqrt{38}<\sqrt{49}$, so $6<\sqrt{38}<7$. Since 38 is closer to 36 than 49, the best whole number estimate for $\sqrt{38}$ is 6. Find a perfect square a little less than 21.6 and one a little more than 21.6. $\sqrt{16}<\sqrt{21.6}<\sqrt{25}$ , so $4<\sqrt{21.6}<5$ . Since 21.6 is closer to 25 than 16, the best whole number estimate for $\sqrt{21.6}$is 5.

 a. Estimate $-\sqrt{32}$   to the nearest whole number b. Estimate $-\sqrt{18}$  to the nearest whole number Find a perfect square a little less than 32 and one a little more than 32. $-\sqrt{25}\g\;-\sqrt{32}\;\g\;-\sqrt{36}$ , so $-6\;\g\;-\sqrt{32}\;\g\;-5$ . Since 32 is closer to 36 than 25, the best whole number estimate for $-\sqrt{32}$ is -6. Find a perfect square a little less than 18 and one a little more than 18. $-\sqrt{16}\;\g-\sqrt{18}\;\g\;-\sqrt{25}$ , so $-4\;\g\;-\sqrt{18}\;\g\;-5$ . Since 18 is closer to 16 than 25, the best whole number estimate for $-\sqrt{18}$   is -4.