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Estimating Square Roots

Find the value of $\sqrt{60}$ to the nearest integer

Look at perfect squares close by

$\sqrt{64}=8$

$\sqrt{49}=7$

64-60=4

60-49=11

64 is the closest to 60 because 4 is less than 11, therefore $\sqrt{60}$ is approximately 8

Note: The actual number is less than 8 because $8^2=64$ 64 > 60

Find the value of $\sqrt{40}$ to the nearest integer

Look at the perfect squares close to $\sqrt{40}$

$\sqrt{49}=7$

$\sqrt{36}=6$

49-40=9

40-36=4

36 is closer to 40 because 4 < 9. Therefore, $\sqrt{40} \approx 6$ .

Note: The actual number is greater than 6 because $6^2=36$ 40>36.