Can you help this character from Shoe take his math test?
In Lesson
8–1, you learned that squaring a number means using that number as a
factor twice. The opposite of squaring is finding a square root. To find a square root
of 36, you must find two equal factors whose product is 36.
The symbol 
, called a radical sign, is used to indicate the square root.
Exponents
can also be used to indicate the square root. 9½ means the same
thing as 
. 9½ is read nine to the one half power. 9½
= 3.
Example
Simplify
each expression.
Alternative Solutions:
Alternative Solutions:
A radical
expression is an expression that contains a square root. You can
simplify a radical expression like 
by using prime
numbers.
A prime number
is a whole number that has exactly two factors, the number itself and 1. A composite number is a
whole number that has more than two factors. Every composite number can be
written as the product of prime numbers. The tree diagram shows one way to find
the prime factors of 225.
When a number is expressed as a product of prime factors, the expression
is called the prime
factorization of the number. Since 3 and 5 are prime numbers, the
prime factorization of 225 is 3 × 3 × 5 × 5.
To simplify , use the following property.
Example
Simplify
each expression.
Alternative Solutions:
Alternative Solutions:
A similar property for quotients can be used to simplify radicals.
Alternative Solutions:
You can use a graphing calculator to evaluate square roots. Press 
and then the number to
find its positive square root.
Example
Aviation Link
6. Pilots use
the formula 
to determine the
distance in miles that an observer can see under ideal conditions. In the
formula, d is the distance in miles and h is the height in feet of the plane.
If an observer is in a plane that is flying at a height of 3600 feet, how far
can he or she see?
Alternative Solutions:
Sumber
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