Transcript Bell Ringer

Bell Ringer
Name all of the sets of numbers to which
each real number belongs.
Natural,Whole, Integer, Rational, Irrational
#1. 4
#2. 3/5
#3. -7/2
#4. √26
Supply Check
I have decided to announce the first
supply check.
 This will happen on FRIDAY, OCTOBER
24
 I will be looking for pencil, piece of paper,
calculator, and red pen.

Continue 10. 1 and 10.2
Radicals and Real Numbers

R drive > Key > Week 11 > Wednesday >
Finish 10.1 and 10.2

File > Save As > P drive > math > Week
Finish 10.1 and 10.2
Simplifying Radicals
Vocabulary
Radical Expression – An expression
that contains a square root
 Radicand – the expression under the
radical sign

Notes

A radicand is in simplest form if it contains no
perfect square factors other than 1. The
following property can be used to simplify square
roots.

Product Property of Square Roots:
 For any numbers a and b, where a ≥ 0 and b ≥ 0, the
square root of the product ab is equal to the product of
each square root.
 Symbols:
 Example:
The Product Property of Square Roots and prime factorization
can be used to simplify radical expressions in which the
radicand is not a perfect square.
Simplify Square Roots:
Example 1)
=
step one: prime factorization of 12
step twp: product property of sq roots
step three: simplify
Your turn: Remember the steps……
step one: prime factorization
step two: product property of sq roots
step three: simplify
Example 2)
The product property can also be
used to multiply square roots:
Multiply Square Roots
Example 3) Find
Your turn: remember the steps
2b)
A fraction containing radicals is in
simplest form if 1) no prime
factors appear under the radical
sign with an exponent greater than
1 and if
2) no radicals are left in
the denominator. Rationalizing the
denominator of a radical
expression is a method used to
eliminate radicals from the
denominator of a fraction.
Rationalizing the Denominator:
3a) Simplify
step one: multiply by a fraction with the
denominator of this fraction in
its numerator and denominator.
•
=
(I will explain)
step two: simplify if necessary
Your turn:
3b)
remember the steps
More Practice:
Simplify:
1)
4)
6)
Write problems and show work on notebook paper.
2)
3)
5)
7)
Example 3
Compare Real Numbers
Example 4
Compare Real Numbers
Your Turn
Practice Comparing Real Numbers
Example 5
Order Real Numbers
Example 6
Order Real Numbers
Your Turn
Practice Ordering Real Numbers
Example 7
Solve Equations
Example 8
Solve Equations
Solve each equation. Round to the nearest
tenth, if necessary.
a. W2 = 169
b.
R2 = 50
Your Turn
Practice Solving Equations
Example 9
Use Real Numbers to Solve Problems
Example 10
Use Real Numbers to Solve Problems
The formula for aspect ratio R is R = s2/A,
where s is the wingspan in feet and A is
the area of the wing. What is the
wingspan of a hang glider if the aspect
ratio is 6.4 and the area of the wing is 40
square feet?
Your Turn
Practice Using Real Numbers to Solve Problems
Homework
Section 10.1 #1-13
Homework
Section 10.1 #1-13