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Introduction to Irrational Numbers

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We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.” √ 3 is an irrational number. √ is the radical sign / symbol, and 3 is called the radicand.

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HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

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In the expression, is the radical sign and 64 is the radicand. If x 2 = y then x is a square root of y. 1. Find the square root: 8 2. Find the square root: -0.2

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3. Find the square root: 11, -11 4. Find the square root: 21 5.Find the square root:

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6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6.82, -6.82

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What numbers are perfect squares? 1 1 = 1 2 2 = 4 3 3 = 9 4 4 = 16 5 5 = 25 6 6 = 36 49, 64, 81, 100, 121, 144,...

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The square root of 4 is 2

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The square root of 9 is 3

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The square root of 16 is 4

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The square root of 25 is 5

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1. Simplify Find a perfect square that goes into 147.

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2. Simplify Find a perfect square that goes into 605.

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Simplify A.. B.. C.. D..

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Now you try some…

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Now you try…

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How do you simplify variables in the radical? Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

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4. Simplify Find a perfect square that goes into 49. 5. Simplify

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Simplify 1.3x 6 2.3x 18 3.9x 6 4.9x 18

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Now you try some…

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Adding & Subtracting Radicals The rules for adding and subtracting radicals are very similar to the rules for adding and subtracting polynomials. The radical / radicand have to match exactly in order to add or subtract.

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Ex. 1:

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Ex. 2:

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Now you try some…

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IMPORTANT If each radical in a radical expression is not in simplest form, simplify them first. Then use the distributive property, whenever possible, to further simplify the expression.

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Ex. 4:

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Ex. 5: Simplify, then use a calculator to verify your answer.

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Ex. 6: Simplify, then use a calculator to verify your answer.

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Now you try some…

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Rational or Irrational? Justify your answer.

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