Symbols

Every radical expression contains three parts:

This expression represents the number we must cube to get 64. Because , we say that

a

3 64

Defn: is the positive (or principal) square root of a. It is the positive number whose square is a.

index

Radicalsymbol radicand

34 64 3 64 4

NOTE: When an index is not shown, it is assumed to be a 2.

You might want to memorize the first few square and cube roots?

1 1

4 2

9 3

16 4

25 5

36 6

49 7

64 8

81 9

100 10

121 11

144 12

3

3

3

3

3

1 1

8 2

27 3

64 4

125 5

Radical Facts: The even power of a

real number is always positive or zero.

Thus, an even root of a negative number is undefined on the set of real numbers.

An odd root of a negative number will always be negative.

4 16

3 8 2

4( 2) 2 2 2 2 16

Keep It Straight!

9 3

9

The negative square root of 9 is -3!

Where the square root of a negative numberis undefined on the set of real numbers.

Now,You’ve Got It!

Radicals with Fractions Keep your cool! It is

easy.

4 4 2

25 525

Just take the square rootof the numerator ANDtake the square root of thedenominator!

Examples:

4

3

16 4

121 11

81 3

27 3

0 0

Remember: it is okay to havea negative radicand if the root odd.. We just get a NEGATIVEANSWER!

Rational or Irrational, that is the question? Some radicals come

out nice and easy.. Others not so nice..

Since there is no number that raised to the third power gives us 12, our calculator has to approximate it:

4 4

3

2401 7 7 7 7 7

12 2.289428485...

If the decimal approximation terminates or repeats it is a rational number.If the decimal approximation does not terminate or repeat, it is called an irrational number.