SOLUTION: Which of these radical expressions are in simplest form? sqrt x^3 / 4, sqrt x / 2, 2 sqrt x / 3, x/2 sqrt x.

Algebra ->  Radicals -> SOLUTION: Which of these radical expressions are in simplest form? sqrt x^3 / 4, sqrt x / 2, 2 sqrt x / 3, x/2 sqrt x.      Log On


   

Question 1095904: Which of these radical expressions are in simplest form?
sqrt x^3 / 4, sqrt x / 2, 2 sqrt x / 3, x/2 sqrt x.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%5E3%29%2F4

Not in simplest radical form because it can be simplified this way:


sqrt%28x%5E2%2Ax%29%2F4

%28sqrt%28x%5E2%29sqrt%28x%29%29%2F4

%28abs%28x%29sqrt%28x%29%29%2F4

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sqrt%28x%29%2F2

That's in simplest radical form.

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2sqrt%28x%29%2F3

That's in simplest radical form

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x%2F%282sqrt%28x%29%29

Not in simplest radical form because it can be simplified this way:

Rationalize the denominator by multipying by sqrt%28x%29%2Fsqrt%28x%29

x%2F%282%2Asqrt%28x%29%29%22%22%2A%22%22sqrt%28x%29%2Fsqrt%28x%29

%28x%2Asqrt%28x%29%29%2F%282%2Asqrt%28x%29%2Asqrt%28x%29%29

%28x%2Asqrt%28x%29%29%2F%282%2Ax%29%29

%28cross%28x%29%2Asqrt%28x%29%29%2F%282%2Across%28x%29%29%29

%28sqrt%28x%29%29%2F2%29

Edwin