Vocabulary
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
The Pythagorean Theorem
What are the two square roots of 64?
+ and - 8
What two integers is √6 between?
2 and 3
Rational, irrational, or not a real number: √9
Rational
What is the algebraic representation of the Pythagorean Theorem?
a^2 + b^2 = c^2
The set of numbers which consists of rational numbers and the set of irrational numbers
Real numbers
What are the two square roots of 361?
+ and - 19
What two integers is -√90 between?
-9 and -10
Rational, irrational, or not a real number: -√9
Rational
The two legs of a right triangle are 3 and 4 units long respectively. What is the length of the triangle's hypotenuse?
5 units
Numbers that can only be written as decimals that do not terminate or repeat
Irrational Numbers
Evaluate: 5(√225 - 10)
25
What is the √330 to the nearest tenth?
18.2
Rational, irrational, or not a real number: √-9
Not a real number
If a right triangle has a leg 15 units long and a hypotenuse 17 units long, how long is the other leg?
8 units
The non-negative square root of a number
Principal Square Root
A karate match is held on a square mat that has an area of 676 square feet. What is the length of the mat?
26 ft.
Each square on Laura's chessboard is 13 square centimeters. A chessboard has 8 squares on each side. To the nearest hundredth, what is the width of Laura's chessboard?
approx. 28.84 cm.
Give an example of an irrational number that is less than -3.
Possible answer:-√30
A traffic helicopter flies 10 miles due north and then 24 miles due east. Then the helicopter flies in a straight line back to its starting point. What was the distance of the helicopter's last leg back to it's starting point?
26 miles
A method of writing very large numbers or very small numbers by using the powers of 10
Scientific Notation
An office building has a square courtyard with an area of 289 square feet. What is the distance around the edge of the courtyard?
68 ft.
A square photo is placed behind a piece of glass that has an area of 20 square inches. To the nearest, what length of frame is needed to go around all edges of the glass?
4.47 in.
Find a real number between 4 and √9
possible answer: 3.5
A construction company is pouring a rectangular concrete foundation. The dimensions of the foundation are 24 ft. by 48 ft. Describe a procedure to confirm that the sides of the foundation meet at a right angle.
Possible answer: Use the Pythagorean Theorem to find the expected length of the diagonal.