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Square Roots
Simplifying Square Roots
Pythagorean Theorem
Real Numbers
Distance & Midpoint Formula
100
Define square root.
A number n is a number m such that m²=n
100
Give an example of how the product property works.
√9x7 = √9 x √7 = 3√7
100
What is the formula for Pythagorean Theorem?
a²+b²=c²
100
Define irrational number
A number that cannot be written as a quotient of two integers
100
What is the distance formula?
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200
What is the square root of 64? 25? 36? 81? 144? What do all of these have in common?
8 - 5 - 6 - 9 - 12 They are all perfect squares
200
Simplify √54
3√6
200
Determine whether the triangle with the given side lengths is a right triangle: a=15 b=8 c=17
Yes, 289=289
200
Are the following rational or irrational? a. √10 b. √25 c. .666666666666 d. ¾ e. √95
a) irrational b) rational c) rational d) rational e) irrational
200
What is the formula for midpoint?
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300
Approximate √51 to the nearest integer
√51≈7
300
Simplify √15/16
√15/√16=√15/4
300
Define hypotenuse, legs, and Pythagorean Theorem
Hypotenuse: the side opposite the right angle Legs: sides that form the right angle Pythagorean Theorem: For any right triangle, the sum of squares of the lengths a and b of the legs equals the square of the length c of the hypotenuse: a²+b²=c²
300
Order the following from least to greatest 4/3 , -2.8, √3 , and -√5
-2.8 , -√5 , 4/3, √3
300
Find the distance between M(6, 3) and N(5, 7)
√17 units or ≈ 4 units
400
Solve the equation 5y²=110
≈ 5
400
Simplify : √300x
10√3x
400
What is side a if side b=30 and side c = 32? Be sure to simplify if necessary.
a= 2√31
400
Complete the statement by using: < , > , = a) 4√3 ? 27/4 b) √0.5 ? 0.5
a) > b) >
400
What is the midpoint of a segment with endpoints (3,8) and (-9, -4)
(-3 , 2)
500
Using the formula ⌡= 0.0625s² to approximate the maximum running speed s (in meters per second) that a person with leg length ⌡ (in meters) can sustain. Find the maximum running speed for a person with a leg length of .64 meter.
3.2m/sec or if approximating ≈ 3
500
Simplify √40/144
24√10
500
A ladder that is 15 feet long is placed against a wall. The bottom of the ladder is 5 feet from the wall. To the nearest foot, how far up the wall does the ladder reach? 1) Draw a diagram and label the lengths and the unknown length as x 2) Solve for x 3) Round your answer to the whole number
1) View diagram 2) x= 10√2 3) ≈ 10
500
solve for x: 216x³=64
2/3
500
Define distance formula and midpoint formula in words.
Distance formula: the distance between two points in a coordinate plan is equal to the square root of the sum of the horizontal change squared and the vertical change squared. Midpoint formula: The coordinates of the midpoint of a segment are the average of the endpoints' x-coordinates and the average of the endpoints' y-coordinates