SOLUTION: I need help! I can't figure out how to do this: Rationalize the denominator and simplify. 49 times the square root of 14 over 21 times the square root of 3

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need help! I can't figure out how to do this: Rationalize the denominator and simplify. 49 times the square root of 14 over 21 times the square root of 3       Log On


   



Question 249022: I need help! I can't figure out how to do this:
Rationalize the denominator and simplify.
49 times the square root of 14 over 21 times the square root of 3

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%2849%2Asqrt%2814%29%29%2F%2821%2Asqrt%283%29%29 Start with the given expression.


%287%2Asqrt%2814%29%29%2F%283%2Asqrt%283%29%29 Reduce 49%2F21 to get 7%2F9


%287%2Asqrt%2814%29%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%29 Multiply both the numerator and denominator by sqrt%283%29


%287%2Asqrt%2814%29%2Asqrt%283%29%29%2F%283%2A3%29 Multiply sqrt%283%29 by sqrt%283%29 to get sqrt%283%29%2Asqrt%283%29=sqrt%283%2A3%29=sqrt%283%5E2%29=3


%287%2Asqrt%2814%29%2Asqrt%283%29%29%2F9 Multiply 3 and 3 to get 9


%287%2Asqrt%2814%2A3%29%29%2F9 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


%287%2Asqrt%2842%29%29%2F9 Multiply 14 and 3 to get 42


So %2849%2Asqrt%2814%29%29%2F%2821%2Asqrt%283%29%29=%287%2Asqrt%2842%29%29%2F9