Perfect Square Roots & Approximating Non-Perfect Square Roots8.NS.2 USE RATIONAL APPROXIMATIONS OF IRRATIONAL NUMBERS TO COMPARE THE SIZE OF IRRATIONAL NUMBERS, LOCATE THEM APPROXIMATELY ON A NUMBER LINE DIAGRAM, AND ESTIMATE THE VALUE OF EXPRESSIONS (E.G., Π2). 

8TH GRADE MATH – MISS. AUDIA

Square Roots - A value that, when multiplied by itself, gives the number (ex. √36=±6). 

Perfect Squares - A number made by squaring an integer.

Integer – A number that is not a fraction.

Remember

The answer to all square roots can be either positive or negative.

We write this by placing the ± sign in front of the number.

What are the following square roots?

√1

√4

√9

√16

√25

√36

√49

√64

√81

√100

√121

√144

√169

√196

√225

Let’s Mix It Up

√36

√121

√1

√9

√64

√225

√4

√25

√196

√169

√16

√49

√100

√81

√144

All Square Roots of Perfect Squares are Rational Numbers!

Rational Numbers – Numbers that can be written as a ratio or fraction. These numbers can also be written as terminating decimals or repeating decimals.

Terminating Decimals – A decimal that does not go on forever (ex. O.25).

Repeating Decimals – A decimal that has numbers that repeat forever

(ex. 0.3, 0.372)

The Square Roots of Non-Perfect Squares are Irrational Numbers.

Irrational Numbers – Numbers that are not Rational.

They cannot be written as ratios or fractions.

They are decimals which never end or repeat.

Examples: π, √2, √83

0 1 2 3 4 5 6

√1

√4 √9 √16 √25

√36

The square roots of perfect squares are rational numbers and can be place on a number line.

The square roots of non-perfect squares are irrational numbers. We cannot pinpoint their location on a number line, however we can approximate it.

0 1 2 3 4 5 6

√1

√4 √9 √16 √25

√36

Approximate where the following square roots would be on the number line: √2, √7, √31

0 1 2 3 4 5 6

√1

√4 √9 √16 √25

√36

Approximate where the following square roots would be on the number line: √2, √7, √31

√2

√7 √31