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Published bySamuel Tyler Modified over 3 years ago

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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

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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.

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**What are the following square roots?**

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√1

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√4

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√9

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√16

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√25

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√36

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√49

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√64

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√81

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√100

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√121

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√144

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√169

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√196

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√225

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Let’s Mix It Up

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√36

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√121

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√1

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√9

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√64

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√225

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√4

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√25

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√196

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√169

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√16

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√49

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√100

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√81

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√144

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**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)

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**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

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**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.

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

√1 √4 √9 √16 √25 √36

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**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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