REVIEW: Perfect Squares

√4

√225

√49

√9

√36

√169

√1

√196

√16

√121

√64

√81

√25

√100

√144

Perfect Square and its Square Root √25 = 5 THE ANSWER!

How do you know if a number is a perfect square?

The square root is a whole number Ex. 1, 2, 3, 4... ✔

✔ ✘ The square root has a terminating decimal Ex. √0.0225 = 0.15 vs. √34 = 5.83095189485 ✔ ✘

✔ ✘ The square root has a repeating decimal Ex. √1/9 = 0.3333333 vs. √67 = 8.18535277187 ✔ ✘

✔ The square Rational Number (can be written as a fraction) Ex. √1/9 = 0.3333333 = ⅓ ✔

√900000 or √90000 ✘ ✔

√90000 Because there is an even number of zeros! So the answer will have half the amount of zero after the square root of 9. =300

√0.00004 or √0.0004 ✘ ✔

√0.0004 Because there is an even number of decimal places! So the answer will have half the amount of decimal places. =0.02

√0.000121 Because there is an even number of decimal places! So the answer will have half the amount of decimal places. =0.011

Estimating the Square Root of Non-perfect Squares

Numbers greater than 1 Ex. √41 or √7.5

Numbers less than 1 Ex. √0.2 or √0.59

Fractions Ex. √7/18

Estimating the Square Root of a Non-perfect Square Find the 2 benchmarks that are perfect squares on either side of the number. Determine the square roots of the benchmarks Find the halfway point for both the top and the bottom of the number line Subtract the top benchmarks and divide it by 2 Add the answer to the first benchmark 4. Place the number that you are trying to estimate the square root for on the left or right side of the halfway point 5. Estimate the square root

a2 + b2 = c2 Pythagorean Theorem