# simplifying radicals

by becky

the following expression shows two radicals being multiplied

how do you simplify the expression (without computing a decimal equivalent):

(sr 13)(sr260)

sr= square root

### Comments for simplifying radicals

 Apr 04, 2011 Multiply and Simplify Radicals by: Staff The question: by Becky how do you do (sr 13)(sr260) sr= square root The answer: The square root of 13 multiplied by the square root of 260 = [√(13)] * [√(260)] Group both square roots together, under one square root sign = [√(13)] * [√(260)] = √(13 * 260) Factor both numbers = √(13 * 13 * 2 * 2 *5) Notice that the factored radicand (the number under the radical symbol) consists of two squared numbers = √(13 * 13 * 2 * 2 * 5) = √(13² * 2² * 5) The square root of 13² is 13. The square root of 2² is 2. = √(13²) * √(2²) * √(5) = 13 * 2 * √(5) = 26 * √(5) The final answer is: 26 * √(5) Check your answer. Use a calculator or use Microsoft Excel The original problem = [√(13)] * [√(260)] can be entered into Excel as follows: = sqrt(13)*sqrt(260) Excel will compute = 58.13777 The final solution to the problem = 26 * √(5) can be entered into Excel as follows: = 26*sqrt(5) Excel will compute = 58.13777 These calculations verify that: = [√(13)] * [√(260)] = 26 * √(5) = 58.13777 Thanks for writing. Staff www.solving-math-problems.com

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