perfect square roots & approximating non-perfect square roots
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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
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