SOLUTION: Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real numbers. 1. square root of 5/3 2. square root

Algebra ->  Square-cubic-other-roots -> SOLUTION: Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real numbers. 1. square root of 5/3 2. square root      Log On


   

Question 118061: Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real numbers.
1. square root of 5/3
2. square root of 12x cubed/5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1

sqrt%285%2F3%29 Start with the given expression


sqrt%285%29%2Fsqrt%283%29 Break up the square root


%28sqrt%285%29%2Fsqrt%283%29%29%28sqrt%283%29%2Fsqrt%283%29%29 Multiply the fraction by sqrt%283%29%2Fsqrt%283%29


%28sqrt%285%29sqrt%283%29%29%2F%28sqrt%283%29sqrt%283%29%29 Combine the fraction


%28sqrt%285%2A3%29%29%2F%28sqrt%283%2A3%29%29 Combine the roots


sqrt%2815%29%2Fsqrt%289%29 Multiply


sqrt%2815%29%2F3 Take the square root of 9 to get 3. Notice how the denominator is a rational number. This is why I multiplied the fraction by sqrt%283%29%2Fsqrt%283%29



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#2


sqrt%2812x%5E3%2F5%29 Start with the given expression


sqrt%2812x%5E3%29%2Fsqrt%285%29 Break up the square root


%28sqrt%2812x%5E3%29%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29 Multiply the fraction by sqrt%285%29%2Fsqrt%285%29


%28sqrt%2812x%5E3%29sqrt%285%29%29%2F%28sqrt%285%29sqrt%285%29%29 Combine the fraction


%28sqrt%2812x%5E3%2A5%29%29%2F%28sqrt%285%2A5%29%29 Combine the roots


sqrt%2860x%5E3%29%2Fsqrt%2825%29 Multiply


sqrt%2860x%5E3%29%2F5 Take the square root of 25 to get 5.


sqrt%284%2A15x%5E2%2Ax%29%2F5 Factor 60 into 4*15 x%5E3 into x%5E2%2Ax


sqrt%284%29sqrt%2815%29sqrt%28x%5E2%29sqrt%28x%29%2F5 Break up the root


%282sqrt%2815%29x%2Asqrt%28x%29%29%2F5 Take the square root of 4 to get 2 and take the square root of x%5E2 to get x

%282%2Ax%2Asqrt%2815%29sqrt%28x%29%29%2F5 Rearrange the terms


%282x%2Asqrt%2815x%29%29%2F5 Combine the roots

So sqrt%2812x%5E3%2F5%29 simplifies to %282x%2Asqrt%2815x%29%29%2F5