1. Square Roots and the Pythagorean Theorem
Section 6.4
Square Roots
and the
Pythagorean Theorem

2. nth Root

3. Square Root Index is ALWAYS 2
The square root of a positive number a is the positive number b whose square is a.
In symbols

4. Square Root Steps Write the radicand in prime factorization.
Group like prime numbers in sets of two (index)
One whole set becomes on prime number outside the radical symbol
Multiply all numbers on the outside together
Multiply all numbers on the inside together

5. Examples
Simplify

6. Examples
Simplify

7. Examples
Simplify

8. Examples
Simplify

9. Examples
Simplify

10. Pythagorean Theorem
Given a right triangle the hypotenuse squared is equal to the sum of each leg squared.

11. Example
Find the missing leg

12. Example
Find the hypotenuse

13. Example
Find the hypotenuse

14. Example
Find the height of the antenna. Round the height to the tenth place.