Page 161 - Algebra

8.5. Radical Expressions
𝑛
The symbol √𝑏 is radical.
n = index
b = radicand
√ = radical sign
REMEMBER:
•
•
For any nonnegative number a and b,
√𝑎𝑏 = √𝑎√𝑏
√𝑎 = √𝑎 𝑏 √𝑏
For any real numbers a and b
222 √𝑎𝑏= √𝑎√𝑏
2 2𝑎 √𝑎
√==2
𝑏 √𝑏
When b ≠ 0
You can solve a radical in the denominator by rationalizing the denominator.
Multiplication and division are similar to multiplying or dividing monomials and binomials.
(√𝑎 + √𝑏) (√𝑎 − √𝑏) are called conjugates. The product of conjugates is always an integer. You can
even use conjugates to solve the denominators.
You can add and subtract radicals with like radicands. Addition and subtraction are done the same way
in which you add and subtract monomials.
Worked Example
Solve the following equation:
√4 − 5𝑥 = 8
Solution:
√4 − 5𝑥 = 8
To remove the radical, square both LHS and RHS (√4 − 5𝑥)2 = 82
4 – 5x = 64 –5x = 64 – 4 x = –12
Page 160 of 177
Algebra I & II