5.4 Irrational Numbers. Irrational numbers Irrational numbers are those that cannot be written as a fraction Irrational numbers have non-terminating or.

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Presentation transcript:

5.4 Irrational Numbers

Irrational numbers Irrational numbers are those that cannot be written as a fraction Irrational numbers have non-terminating or non-repeating decimals The square root of any prime number is irrational π is irrational

Not every square root is irrational Numbers like 36 and 81 are called perfect squares

Perfect squares 0 2 = = = = = = = = = = = = = = = = 225

Simplifying square roots Product rule

Examples: Simplify

Multiply

Dividing square roots

Examples: Divide

Addition/Subtraction To add or subtract square roots the radicand (the number under the radical) must be the same Then add/subtract the numbers in front of the radicals

Examples: Add or subtract

More addition If the radicands are different try to simplify first

Examples: Simplify then add

Rationalizing If there is a radical in the denominator of a fraction you can simplify or rationalize by multiplying both the numerator and the denominator by the radical

Examples: Rationalize

Other roots

HW: p. 234/1-66 evens