SOLUTION: Find the square root of a fraction. Example: cube to the square root of 8 over 27.

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Find the square root of a fraction. Example: cube to the square root of 8 over 27.      Log On


   

Question 255880: Find the square root of a fraction.
Example: cube to the square root of 8 over 27.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose we are given
sqrt%28a%2Fb%29
the rules allow you to separate to get
sqrt%28a%29%2Fsqrt%28b%29
Or as fractional exponents, we can say
%28a%2Fb%29%5E%28x%2Fy%29.
From here you can reduce a/b if appropriate or apply the powers.
EX: sqrt%288%2F27%29
since you can't reduce the terms, split them apart as
%28sqrt%288%29%29%2F%28sqrt%2827%29%29
and then simplify to get
2sqrt%282%29%2F%283sqrt%283%29%29
rationalizing the denominator gets us
2sqrt%286%29%2F3
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ex: %28sqrt%288%2F27%29%29%5E3
taking square roots first, we get
%282sqrt%282%29%2F3sqrt%283%29%29%5E3
second, apply the cube power to get
%288%2A2sqrt%282%29%29%2F%2827%2A3sqrt%283%29%29
which is
%2816%2F81%29%2A%28sqrt%282%29%2Fsqrt%283%29%29
rationalized, it is
16sqrt%286%29%2F243