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Approximating square roots

# Approximating square roots - Simplifying square roots...

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Approximating square roots To find the square root of a number that is not a perfect square, it will be necessary to find an  approximate  answer by using the procedure given in Example .  Example 1 Approximate  Since 6 2  = 36 and 7 2  = 49, then  is between  and  Therefore,  is a value between 6 and 7. Since 42 is about halfway between 36 and 49, you can  expect that  will be close to halfway between 6 and 7, or about 6.5. To check this estimation, 6.5  × 6.5 = 42.25, or about 42.  Square roots of nonperfect squares can be approximated, looked up in tables, or found by using a  calculator. You may want to keep these two in mind:
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Unformatted text preview: Simplifying square roots Sometimes you will have to simplify square roots, or write them in simplest form. In fractions, can be reduced to . In square roots, can be simplified to . There are two main methods to simplify a square root. Method 1: Factor the number under the into two factors, one of which is the largest possible perfect square. (Perfect squares are 1, 4, 9, 16, 25, 36, 49, …) Method 2: Completely factor the number under the into prime factors and then simplify by bringing out any factors that came in pairs....
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