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Simplifying Radicals SPI 3102.2.1 Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.

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Simplifying Radicals Until now, all of the square roots we have encountered have been perfect squares. Other than perfect squares, the result of taking the square root of a number results in a decimal answer. Unless otherwise specified, all answers from this point on, will be written in simplest radical form. Decimal answers will not be acceptable. We will also be simplifying cube roots, fourth roots, etc. (nth roots).

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Simplifying Radicals Before we begin, there is some basic terminology you will need to know. n x radical sign radicand index If there is not an index written on the radical, the index is understood to be 2, which means it is a square root.

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Simplify. Write 50 as the product of 2 numbers, one of which is a perfect square. Take the square root of the number that is a perfect square; write that number in front of the square root sign. The number that is not a perfect square stays under the radical sign.

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Simplify.

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What if the index is larger than 2?

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Simplify. Write 50 as the product of 2 numbers, one of which is a perfect CUBE. Take the cube root of the number that is a perfect cube; write that number in front of the square root sign. The number that is not a perfect cube stays under the radical sign.

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Simplify.

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