1. Simplifying Radical Expressions
Algebra 1

2. The positive and negative square roots
Square Root of a Number
If b 2 = a, then b is a square root of a.
Meaning
Positive
Square Root
Negative
The positive and negative square roots
Symbol
Example

3. Simplifying Radical Expressions

4. Simplifying Radical Expressions
A radical has been simplified when its radicand contains no perfect square factors.
Test to see if it can be divided by 4, then 9, then 25, then 49, etc.
Sometimes factoring the radicand using the “tree” is helpful.

5. Steps Try to divide the radicand into a perfect square for numbers
If there is an exponent make it even by using rules of exponents
Separate the factors to its own square root
Simplify

6. Simplify:

7. Simplify:

8. Simplify:

9. Simplify:
Square root of a variable to an even power = the variable to one-half the power.

10. Simplify:
Square root of a variable to an even power = the variable to one-half the power.

11. Simplify:

12. Simplify:

13. Simplify:

14. Simplify:

15. Simplify:

16. Simplify:

17. Simplify:

18. Simplify:

19. Simplify:

20. Simplify:

21. Terminology:
square root: one of two equal factors of a given number. The radicand is like the “area” of a square and the simplified answer is the length of the side of the squares.
Principal square root: the positive square root of a number; the principal square root of 9 is 3.
negative square root: the negative square root of 9 is –3 and is shown like
radical: the symbol which is read “the square root of a” is called a radical.
radicand: the number or expression inside a radical symbol is the radicand.
perfect square: a number that is the square of an integer. 1, 4, 9, 16, 25, 36, etc… are perfect squares.
irrational number: a number whose decimal form is nonterminating and nonrepeating.
Rational number: a number that can be written in the form a/b, where a and b are integers (b cannot equal 0)
radical expression: an expression that contains a radical.

22. Simplify:

23. Simplify:

24. Simplify:

25. Simplify:

26. Simplify: