NOTES: Simlifying Radicals with Variables

Integrated Algebra

NOTES: Simplifying radicals with variables Name

The same rules apply for simplifying radicals when variables are a part of the expression.

You need to remember what the relationship is between a variable and its square root. b 2 = b  b and b2 = b

EX: c2 = c x2 = x m2 = m

When you try to simplify a radical term with variables, separate the variables in groups of two.

EX: a2b2 = a2 b2 EX: 4x2 = 4 x2

a b = ab 2 x = 2x

Sometimes the groups are uneven, and there is a variable left under the radical sign.

EX: 16y = 16 y

4 y = 4 y

EX: 5a 4 = 5 a 2 a 2

5 a a = a 2 5

EX: 24y 3 = 4 6 y 2 y

2 6 y y = 2y 6y Integrated Algebra

TRY: a) 49x3 b) 40ab 2

c) x 2 y 4 d) 25a

e) 6x 3 f) 10a 5

g) 8m4 n3 h) 100x8 Integrated Algebra

HOMEWORK: Simplifying radicals with variables Name

Simplify each radical.

1. 18y 3 z 2. 100a 2b 4c

3. 75m3n5 4. 36xy 2

5. 12a 2 6. 50x 5 y 3

7. a 2 8. 16x 2 y

9. 50m3 n 4 p 10. 27ab3c 6

11. 9a 2bc 4 12. 144c 3