Rationalize Non-Perfect Squares

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Presentation transcript:

Rationalize Non-Perfect Squares

What is a square root? 5 and 5 Two identical factors of a number. What if it is a Non-Perfect Square???? You can approximate to a decimal Or you can simplify the answer with a method called Rationalizing (or ‘extracting perfect squares’) 5 and 5

Perfect Squares: KNOW 1-20 and their square roots. 1,4,9,16,25,36,49,64,81,100, 121, 144,169,196,225,256,289,324, 361,400

Rationalizing = extracting perfect squares We are going to “simplify” the radical (square root #) as much as possible. Break the number into its “perfect square” factors and simplify those, leave the non-perfect factors inside the radical Find List the factors of 20: 1· 20, 2· 10, 4· 5 Select the factors 4 and 5 because 4 is the only perfect square factor of 20 Break 20 up into the factors, simplify the perfect square

Prove that this is true… 2 • 2 = 4 4 • 5 = 20

Find the This is not a perfect square. Think of all the perfect square factors: 16 times 3 4 times 12 The BEST perfect square factor is 16 because it is largest

Find the This is not a perfect square. Think of all the perfect square factors: 100 times 2 25 times 8 The BEST perfect square factor is 100 because it is largest

Find the What if you used 25 times 8 instead of 100 times 2? It’s ok!! You will just have to rationalize again, like reducing a fraction twice Now notice 8 still has perfect square factors, so rationalize 8

Rationalize the following: