# use the product rule to simplify the radical

label Algebra
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schedule 1 Day
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square root of 60

Jul 23rd, 2015

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According to the product rule for radicals, if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and n is a natural number, then

$\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab}$

The prime factorisation of 60 is

60 = 2 x 2 x 3 x 5 = 4 x 15

$\\ \sqrt{60}=\sqrt{4\times15}\\ \\ Applying\hspace{5} the\hspace{5} product\hspace{5} rule\hspace{5} for\hspace{5} radicals\\ \\ \sqrt{60}=\sqrt{4}\times\sqrt{15}\\ \\ \sqrt{60}=2\sqrt{15}\\$

ANSWER:  $\\ \sqrt{60}=2\sqrt{15}\\$

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Jul 24th, 2015

thanks i see what i did wrong

Jul 24th, 2015

You are welcome :)

Jul 24th, 2015

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Jul 23rd, 2015
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Jul 23rd, 2015
Nov 19th, 2017
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