Transcript POWERPOINT JEOPARDY - Sage Middle School

Rational
Exponents
Rational vs.
Irrational
Mystery ??
Complex
Number i
Real World
Problems
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What do rational exponents
represent?
Answer
•Roots
•Radicals
•Is “square roots” a
correct answer?
Rewrite the following expression
using rational exponents, then
simplify it:
Answer
Simplify the following expression
using your knowledge of rational
exponents.
(-3y1/3)(-2y1/2)
Answer
5/6
6y
True or False??
Answer
True
True or False??
Answer
True
Rational + Rational=??
Irrational +Irrational =??
Answer
Rational
Irrational and rational
example: √2 - √2 = 0
Rational +Irrational=??
Answer
Irrational
Is this always the case?
Are Irrational numbers Real?
That is can we place them
on a number line?
Give an example.
Answer
Yes, irrational numbers are
real; we can place them on a
number line.
(Recall the ruler activity).
Draw a right triangle with an
irrational hypotenuse length.
Answer
(Compliments of Google.com)
Define rational number.
Define irrational number, and
give an example.
Answer
Rational number: def: A number that can be
written in the form a/b, where a, b are integers
and b≠ 0
Irrational number: def: a number that cannot
be written in the form a/b, where a, b are
integers and b≠ 0. An irrational number has a
non-repeating decimal.
Example: pi, sqrt 2, sqrt 15
Simplify the expression
8-4/3
Answer
1/16
Rewrite the following in
radical form:
a(b4+1)-1/2
Answer
Which letters represent
irrational numbers and
why?
a.3.1415926454…..
b..66666666……
c..7317311731117311111
…
Answer
d..123123123123……
a. and c. represent irrational
numbers. We know this because
the decimals are non-repeating.
Simplify
i^49
Answer
i
Simplify
(7+6i)(3-2i)(3i)
Answer
-12+99i
Simplify
i^14
Answer
i^2
Simplify
(2+3i)+(4-i)
Answer
6+2i
Simplify
(7+4i)-(8-3i)
Answer
1+7i
Simplify
Define a complex number
Answer
Any number a+bi where
a and b are real numbers.
Simplify
(5+7i)(6-7i)
Answer
79+7i
Cindy has a piece of ribbon
that is 4/5 of a foot long. How
long would each piece be if
she cut the ribbon in half?
Answer
Each half of the ribbon would
be 4.8 inches long
Tool box problem: Longest Screwdriver
A toolbox has length L, width W, and height H.
The length D of the longest screwdriver that will
fit inside the box is given by:
D = (L2 + W2 + H2)1/2
Find the length of the longest screwdriver that
will fit in a 4 in. by 6 in. by 12 in. box.
Answer
14 inches
Find the error
(2+4i)(3-6i)
=6-12i+12i-24i
=6-24i
Answer
(2+4i)(3-6i)
=6-12i+12i-24i^2
=6-24(-1)
=30
Where do irrational
numbers originate from?
What happened to the man
who promoted irrational
numbers?
Answer
Irrational numbers originate from mathematicians who
were working with the Pythagorean Theorem. They
discovered that a right triangle with legs of unit length
1 would have a hypotenuse of the square root of two.
The man who promoted irrational numbers, Greek
mathematician Hippasus, was taken to sea and never
returned!
Jared wants to cut a rectangle of paper
diagonally. He wants the diagonal to be
square root 5 inches in length. What lengths,
in inches, do each of the sides of the
rectangle need to be to give Jared the
diagonal that he wants?
Answer
The sides of the rectangle need to be the square root of
4 inches and 1 inch.