How do you simplify #sqrt(16/27)*sqrt(5/3)#?

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Answer 1 · 2018-02-05T02:46:57

#color(purple)((4/9) * sqrt5#

To simplify #sqrt(16/27) * sqrt(5/3)#

According to theory of indices,

#a^m * b^m = (a*b)^m#. Also, #a^m * a^n = a^(m+n)#

Using the above properties,

#sqrt(16/27) * sqrt5/3) = (16/27)^(1/2) * (5/3)^(1/2)#

#=> ((16/27)(5/3))^2 = ((16 * 5) / (27 * 3))^(1/2)#

#=> ((4 * 4 * 5) / (9 * 9))^(1/2) = color(purple)((4/9) * sqrt5#

Answer 2 · 2018-02-05T02:50:00

The answer is #(4sqrt(5))/9#, or about #0.994#.

Radicals that are multiplied together can be condensed together if you multiply their radicands (the stuff under the radical):

#sqrt(16/27)*sqrt(5/3)#

#sqrt((16*5)/(27*3))#

#sqrt(80/81)#

#sqrt(80)/sqrt(81)#

#sqrt(16*5)/9#

#(4sqrt(5))/9~~0.99381...#