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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

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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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