• The square function and the square root function are inverses of each
other. This means that one
'undoes' the other and vice versa
• A number c is a square root of a if and only if c2 = a
• This is true of any root functions. i.e. A number c is said to be an nth root
of a if and only if cn = a
• Properties of Radicals :
If n is even,
If n is odd,
• In some exercises, the book takes the stand that it
as sumes no radicands are formed by raising
negative quantities to even powers . Really, they are just getting lazy because
they don't want to
write the proper solution to a problem like 
They make this assumption so they can drop
the absolute value sign . This is not good practice
• Example. Simplify 
• Example. Simplify 
• Example. Simplify 
• Example. Simplify 
• Example. Simplify 
The Pythagorean Theorem:
• The sum of the squares of the lengths of the legs of a right triangle is equal
to the square of the
length of the hypotenuse
• a^2 + b^2 = c^2
• Example, page 45 number 60 (see book)
We have to assume this buckle is actually straight, which in reality it probably
isn't completely
There are 5280 feet in 1 mile
The bridge actually lengthens by two feet . Assuming it does so symmetrically,
this gives
us an additional foot on each side
Making a diagram of the problem with appropriate constants filled in we have…
Therefore the height of the buckle is given by
