1. Radicals

2. Radicals We say the square root of a or root a.
The symbol is a radical.
The positive number a is the radicand.
We say the square root of a or root a.

3. The square root of a number n is the number which, when squared is n.
For example :
5 and -5 are both the square root of 25,
since 52 = 25 and (-5)2 = 25. √ 25
= 5 and -5

4. - The symbols: indicates the positive root indicates the negative root
indicates both roots

5. Some examples: 8
– 6
± 2

6. Why can’t we find a square root for -36... in other words can b2= -36?
62 = 36
(-6)2 = 36
6(-6) = -36
The square of a number can never be negative.
Therefore, the square root of a negative number does not exist in the real numbers.

7. Radical Rules:

8. Product Rule--
The square root of a product is equal to the the product of the square roots.

9. Quotient Rule--
The square root of a quotient is equal to the quotient of the two radicals.

10. Important Products:
n is positive
= n

11. Radicals are simplified when:
1) the radicand has no perfect square factors
2) the denominator of a fraction is never under a radical.
The product and quotient rules allow radical expressions to be simplified.

12. #1 “Take out” perfect square factors
Rewrite the radicand as a product of its factors; with the largest perfect square factor possible. Use the product rule to simplify the root of the perfect square as a rational number, leaving the other factor under the radical.

13. #2 Rationalize the denominator:
To create a fraction with a rational denominator, multiply both numerator and denominator by the the irrational number found in the denominator of the fraction.

14. Comparison with variables
Examples
Comparison with variables