Real World Problems Complex Number i Mystery ?? Rational vs. Irrational Rational Exponents 50 40 30...
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Real World Problems
Complex Number iMystery ??Rational vs.
IrrationalRational
Exponents
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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
6y5/6
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…d..123123123123……Answer
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 wherea 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.