SOLUTION: Simplify by combining like terms. 1) 5 square root of 8 MINUS 2 square root of 50 PLUS square root of 18 2) 3 square root of 5 MINUS square root of 45

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify by combining like terms. 1) 5 square root of 8 MINUS 2 square root of 50 PLUS square root of 18 2) 3 square root of 5 MINUS square root of 45      Log On


   

Question 124528: Simplify by combining like terms.
1) 5 square root of 8 MINUS 2 square root of 50 PLUS square root of 18

2) 3 square root of 5 MINUS square root of 45
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
1) 5sqrt%288%29-2sqrt%2850%29%2Bsqrt%2818%29
The technique to use here is to factor the quantity under the radical (the radicand) looking for perfect squares in the factors. When you do find a factor that is a perfect square, take its square root and move the result outside of the radical.
Like this:
5sqrt%288%29+=+5sqrt%282%2A4%29 the 4 is a perfect square and its square root is 2, so you can rewrite this as:
5sqrt%288%29+=+5sqrt%282%2A4%29=5%2A2sqrt%282%29+=+10sqrt%282%29
See the idea?
Simplifying, we get:
10sqrt%282%29-10sqrt%282%29%2B3sqrt%282%29=3sqrt%282%29
2) Simplify:
3sqrt%285%29-sqrt%2845%29=+3sqrt%285%29-sqrt%285%2A9%29=3sqrt%285%29-3sqrt%285%29+=+0