123
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Rules for Radicals

Here's the rule for multiplying radicals:

(nth root of a)(nth root of b) = (nth root of ab)

* Note that the types of root, n, have to match!

Here are a few examples of multiplying radicals:

( sqrt(2) )( sqrt(8) ) = sqrt(2*8) = sqrt(16) = 4
Pop these into your calculator to check!

(cube root of 2)(cube root of 4) = (cube root of 2*4) = (cube root of 8) = 2

( sqrt(5) )( sqrt(7) ) = sqrt(5*7) = sqrt(35)

( sqrt(3) )( sqrt(3) ) = sqrt(3*3) = sqrt(9) = 3

( 2*sqrt(2) )( 3*sqrt(50) ) = ( 2*3 )( sqrt(2) )( sqrt(50) ) = 6*sqrt(2*50) = 6*sqrt(100) = 6*10 = 60

(If you don't believe me, grab a calculator to check!)