TOTALLY RADICAL DUDE!!!!
Practice with Radicals Coefficient radicand Example: 2 36 The coefficient is 2. The radicand is 36. 7 Assume the coefficient is 1. The radicand is 7. The expression n a is called the principal nth root of a (abbreviated as the nth root of a); n is the index of the radical expression n a . The number a is the radicand, and is the radical. When there is no n value given it is always 2 meaning square root. For our purposes n will always =2. When evaluating the square root from the radical form we are always looking for the principle root (positive). If the radicands are perfect squares simplify them during the exponent phase of the order of operations. I. SIMPLIFYI NG BY FACTORING Sometimes the radicand can be simplified by factoring into perfect squares. Examples: 1.
50 = 25 ⋅ 2 = 25 ⋅ 2 = 5 2
2.
27 = 9 ⋅ 3 = 3 3
3. 12 = 4 ⋅ 3 = 2 3 Practice 1. 125 2.
4.
216
5.
45
80
3. − 75m3 p 2
6.
96 9.
7.
96
48 10. 192
8.
72
Variables can be included as part of the radicand. They are factored and moved to the coefficient just like the numbers. Examples 1.
150r = 2g3g5g5gr = 5 6r
2.
9 x 5 = 3g3gxgx gxgxgx = 3 x 2 x
Practice 1.
36x
7. − 12x
2.
96m3
8. − 24a 4b 2 c3
3.
25x 4
9.
4.
36x 3 y 2
10. − 75m3 p 2
5. − 8a
6.
x10 y 5
27k 3