Real World Problems Complex Number i Mystery ?? Rational vs. Irrational Rational Exponents

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. (-3y 1/3 )(-2y 1/2 ) Answer

6y 5/6

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(b 4 +1) -1/2 Answer

Which letters represent irrational numbers and why? a ….. b …… c … d …… 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 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 = (L 2 + W 2 + H 2 ) 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.