1 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
2 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.
35 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)
36 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
37 The square roots of perfect squares are rational numbers and can be place on a number line. √1√4√9√16√25√36The square roots of non-perfect squares are irrational numbers. We cannot pinpoint their location on a number line, however we can approximate it.
38 Approximate where the following square roots would be on the number line: √2, √7, √31 √1√4√9√16√25√36
39 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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