SOLUTION: I need some help understanding how to do these problems. Simplify: 2 square root of 12+ 4 square root of 27 and simplify: square root of 20 over 5 - 1 over square root of 5

Algebra ->  Radicals -> SOLUTION: I need some help understanding how to do these problems. Simplify: 2 square root of 12+ 4 square root of 27 and simplify: square root of 20 over 5 - 1 over square root of 5       Log On


   

Question 91333: I need some help understanding how to do these problems.
Simplify: 2 square root of 12+ 4 square root of 27
and simplify: square root of 20 over 5 - 1 over square root of 5
thanks a million
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
2sqrt%2812%29%2B4sqrt%2827%29
Another way to write this is as follows:
2sqrt%282%5E2%2A3%29%2B4sqrt%283%5E2%2A3%29
Now, apply this property:
sqrt%28x%5E2%29=x
This gives you:
2%2A2sqrt%283%29%2B4%2A3sqrt%283%29
Simplifying:
4sqrt%283%29%2B12sqrt%283%29
Now that each term is the square root of the same thing, they can be combined:
highlight%2816sqrt%283%29%29
================================================
%28sqrt%2820%29%2F5%29-%281%2Fsqrt%285%29%29
%28sqrt%282%2A2%2A5%29%2F5%29-%281%2Fsqrt%285%29%29
Rationalize the denominator of the second term:
%282sqrt%285%29%2F5%29-%28sqrt%285%29%2F5%29
Now perform the subtraction and you are done:
highlight%28sqrt%285%29%2F5%29
Good Luck,
tutor_paul@yahoo.com