SOLUTION: what does 2 radical sign 45 minus 2 radical sign 5 equal

Algebra ->  Radicals -> SOLUTION: what does 2 radical sign 45 minus 2 radical sign 5 equal       Log On


   

Question 513981: what does 2 radical sign 45 minus 2 radical sign 5 equal
Answer by drcole(72) About Me  (Show Source):
You can put this solution on YOUR website!
I think that you are being asked to simplify the expression:
+2%2Asqrt%2845%29+-+2%2Asqrt%285%29+
The important thing to remember here is that you can break up the square root of a product into a product of square roots:
+sqrt%28ab%29+=+sqrt%28a%29%2Asqrt%28b%29+
(Note: it is NOT true that sqrt%28a+%2B+b%29+=+sqrt%28a%29+%2B+sqrt%28b%29 --- for example, sqrt%289+%2B+16%29 does not equal sqrt%289%29+%2B+sqrt%2816%29)
We want to break up 45 into a product of a number times a perfect square. One way to do this is:
45+=+9+%2A+5
So sqrt%2845%29+=+sqrt%289+%2A+5%29+=+sqrt%289%29%2Asqrt%285%29+=+3%2Asqrt%285%29+
Thus we can rewrite our original expression as: