# Perfect Square Roots & Approximating Non-Perfect Square Roots

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Perfect Square Roots & Approximating Non-Perfect Square Roots
8.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
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

The square roots of perfect squares are rational numbers and can be place on a number line.
√1 √4 √9 √16 √25 √36 The square roots of non-perfect squares are irrational numbers. We cannot pinpoint their location on a number line, however we can approximate it.

Approximate where the following square roots would be on the number line: √2, √7, √31
√1 √4 √9 √16 √25 √36

Approximate where the following square roots would be on the number line: √2, √7, √31
√1 √2 √4 √7 √9 √16 √25 √31 √36

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