SOLUTION: sqrt 27-sqrt 48

Algebra ->  Radicals -> SOLUTION: sqrt 27-sqrt 48      Log On


   



Question 497716: sqrt 27-sqrt 48
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given Problem:
.
sqrt%2827%29-sqrt%2848%29
.
Factor the terms inside each radical. Look for factors that are perfect squares (in this problem they are 9 and 16).
.
sqrt%289%2A3%29-+sqrt%2816%2A3%29
.
Split each of the radicals into the product of the radicals of its factors:
.
sqrt%289%29%2Asqrt%283%29-sqrt%2816%29%2Asqrt%283%29
.
Determine the square roots of the two radicals containing 9 and 16:
.
3%2Asqrt%283%29-+4%2Asqrt%283%29
.
Factor out the square root of 3 because it is common to both terms:
.
sqrt%283%29%2A%283-4%29
.
Combine the two terms in the parentheses:
.
sqrt%283%29%2A%28-1%29
.
Multiply the -1 times the square root of 3 and use a calculator to determine the decimal value of the square root of 3:
.
-sqrt%283%29+=+-1.732050808
.
Hope this helps you to understand how to do this problem and others like it.