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.