1. Roots of Real Numbers

2. Simplify radicals. Use a calculator to approximate radicals.
Roots of Real Numbers
Simplify radicals.
Use a calculator to approximate
radicals.

3. Real Life Example 1: OCEANOGRAPHY
The speed of a wave can be estimated using the formula , where I is the length of the wave in feet. This is an example of an equation that uses a square root.

4. Key Concepts The symbol indicates an nth root.
Some numbers have more than one real nth root. For example, 36 has two square roots, 6 and -6. When there is more than one real root, the nonnegative root is called the principal root.
Radical sign
index
radicand !

5. Key Concepts
The chart below gives a summary of the real nth roots of a number b. n
if b >0
if b<0
b = 0
Even
One positive root, one negative root
No real roots
is not a real #
One real root, 0
Odd
One positive root, no negative roots
no positive roots, one negative root

6. Example 1: b.) c.) d.) is not a real number Simplify. Answers: a.)
(Find the square root of 16, then divide the exponent on the variable by the index. The index is 2.)
b.)
c.)
(Find what number can be multiplied by itself 5 times. Then divide the exponents on each variable.)
d.) is not a real number

7. Example 2:
REMEMBER: the general rule is to divide the exponent on the inside by the index!!
Simplify.
a.)
Since the index is even, the principal root is nonnegative. Since t could be negative, you must take the absolute value of t to identify the principal root.
b.)

8. Example 3: PHYSICS
The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula , where L is the length of the
pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. Find the value of T for a 1.5 foot-long pendulum.
Answer: about 1.36 s