Pre-Algebra Demystified

square root of a number. The radical sign (

pffiffi
) is used to indicate the square
root of a number, so

ffiffiffiffiffi

16

p

¼4 because 4^2 ¼16 and

ffiffiffiffiffi

25

p
¼5 because 5^2 ¼25.
Numbers such as 1, 4, 9, 16, 25, 36, 49, etc., are called perfect squares
because their square roots are rational numbers.
The square roots of other numbers such as

ffiffiffi

2

p

,

ffiffiffi

3

p

,

ffiffiffi

5

p
, etc., are called
irrationalnumbers because their square roots are infinite, non-repeating dec-
imals. For example

ffiffiffi

2

p

¼1.414213562...and

ffiffiffi

3

p
¼1.732050808.... In
other words, the decimal value of

ffiffiffi

2

p

cannot be found exactly.

Math Note: The easiest way to find the square root of a number is

to use a calculator. However, the square root of a perfect square can be

found by guessing and then squaring the answer to see if it is correct.

For example, to find

ffiffiffiffiffiffiffiffi

196

p

, you could guess it is 12. Then square 12.

122 ¼144. This is too small. Try 13. 13^2 ¼169. This is still too small,

so try 14. 14^2 ¼196. Hence,

ffiffiffiffiffiffiffiffi

196

p

¼14.

The set of numbers which consists of the rational numbers and the
irrational numbers is called thereal numbers.

The Pythagorean Theorem

The Pythagorean theorem, an important mathematical principle, uses right
triangles. Aright triangleis a triangle which has one right or 90oangle. The
side opposite the 90oangle is called thehypotenuse.
The Pythagorean theorem states that for any right triangle c^2 ¼a^2 þb^2 ,
where c is the length of the hypotenuse and a and b are the lengths of its sides
(see Fig. 9-23).

If you need to find the hypotenuse of a right triangle, use c¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a^2 þb^2

p
.If
you need to find the length of one side of a right triangle, use a¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

c^2 
b^2

p
or
b¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

c^2 
a^2

p

.

CHAPTER 9 Informal Geometry 183

Fig. 9-23.