Precalculus Skill Builders Vol 1 Solutions

7. Simplifying and Combining Radicals
Example: Simplify 288 .
When you are asked to write a radical in simpler form, the real task is to reduce the number
under the radical sign as much as possible by taking perfect squares outside the radical.
Solution: Simplify 288 . Find the factorization of 288, choosing perfect
squares as factors whenever possible.
288 = 4 ! 4 ! 9 ! 2
288 = 4 4 9 2
288 = 2 ! 2 ! 3! 2
288 = 12 2
Rewrite the following as radicals in simpler form.
1. 1200 [ 20 3 ] 2. 845 [ 13 5 ]
3. a 3 b 5 [ ab 2 ab ] 4. x 7 b 9 [ x 3 b 4 xb ]
Example: Simplify 3 125 ! 2 80 .
Solution:
First simplify each radical separately and then combine like terms.
3 125 = 3 25 5 = 15 5
2 80 = 2 16 5 = 8 5
3 125 ! 2 80 = 15 5 ! 8 5 = 7 5
Simplify the following expressions.
5. 5 + 18 [ 5 + 3 2 ] 6. 54 + 294 [ 10 6 ]
7. 18 + 108 + 50 + 48
[ 8 2 + 10 3 ]
8. ( 99 ) 2 [ 99 ]
9. ( 12)( 75) [ 30 ] 10. ( 20)( 80) [ 40 ]
11. ( 50)( 98) [ 70 ]
Pre-Calculus with Trigonometry