Download Pythagorean Theorem and its applications

Name _________________________Date____________ Block____
UNIT 2 STUDY GUIDE
Review: Working with Radicals
SQUARE ROOTS
M8N1A.) Find square roots of perfect squares.
M8N1E.) Recognize and use the radical symbol to denote the positive square root of a positive number.
M8N1F.) Estimate square roots of positive numbers.
IRRATIONAL NUMBERS
M8N1C.) Recognize square roots as points and lengths on a number line.
M8N1D.) Understand that the square root of 0 is 0; every positive number has two square roots that are opposite in
sign.
M8N1H.) Distinguish between rational and irrational numbers.
PYTHAGOREAN THEOREM
M8G2A) Apply properties of right triangles, including the Pythagorean Theorem.
M8G2B) Recognize and interpret Pythagorean Theorem as statement about areas of squares on the sides of a right
triangle.
A.) Estimate the solution and graph the following numbers on the number line below.
1)
8
3)
2) - 18
2
0
B.) Define a perfect square and provide 2 examples.
It is any number multiplied by itself. The perfect square of 2 would be 4 and the
perfect square of 13 would be 169.
C.) Name the sets of numbers to which each number belongs: whole numbers (W),
integers (I), rational numbers (Q) and/or irrational numbers (IR).
1) 8 – W, I, Q
3)
2
-Q
3
2) -5 – I, Q
5) - 25 - I, Q
6) -3.5- I, Q
4)
5 - IR
D.) A baseball diamond is actually a square. The distance between bases is 90 feet.
When a runner on first base tries to steal second, a catcher has to throw from home to
second base. How far is it between home and second base?
a2 + b2 = c2  902 + 902 = 16200 = √16200 = 127.28 ft
Name _________________________Date____________ Block____
GUIDE
UNIT 2 STUDY
E.) The National Safety Council recommends placing the base of a ladder one foot from
the wall for every three feet of the ladder’s length. How far away from a wall should
you place a 15-foot ladder? How high can the ladder safely reach?
a2 + b2 = c2  The ladder is the hypotenuse of the right triangle formed against the
wall. The wall would create a leg and the ground would create the other leg. C2 = 15
ft. the distance from the wall would be 5 feet due to the NSC’s recommendations.
(15 feet divided by 3 feet = 5 feet). So 52 + b2 = 152  25 + b2 = 225 so b2 = 200 so b =
√200 or 14.14 ft
F.)Draw a right triangle and label the legs and the hypotenuse.
G.) Simplify and rewrite with positive exponents.
5a 2b3 y 1

H.) Simplify:
a. 4 5 - 7 5
-3√5
b.
3

5
I.) Tri–M is building a garden with an area of 225 sq. ft.
What are the dimensions of the garden if it is a square?
Area = L x W = 225 so √225 = 15 ft
J.) Evaluate each expression. Circle your final answers.
1.
= √49 = 7
X
=
=
Name _________________________Date____________ Block____
GUIDE
= 10 – 5 = 5
2.
3.
225 = 15
4. 4 3  6 3
5.
UNIT 2 STUDY
= - 2√3
= 11 + 16 = 27
K.) What is the Pythagorean Theorem? What is it used for?
a2 + b2 = c2  The Pythagorean Theorem is used when dealing with right triangles,
either to find the legs of the triangle or the hypotenuse of the triangle.
L.) Write the following in scientific notation:
a. 12, 300,000,000
b. .000000725
1.23 x 1010
7.25 x 10-7
c. 245,900,000
2.459 x 108
M.) Simplify the quotient and write the answer in scientific notation:
( 8 x106 )  (4 x 10²)
8 ÷ 4 = 2 and 106 ÷ 102 = 104
So your final answer is 2 x 104