Simplifying Radicals and
Rationalizing Denominators
Rationalizing Denominators
Simplify √8
What is 2√2
Write the Pythagorean Theorem
What is a^2 + b^2 = c^2
In common English, describe
a) What the distance between two points is and
b) What the midpoint between two points is.
What is:
a) how far apart two points are
b) The halfway point between two points.
If c^2 < a^2 + b^2, this type of triangle is formed.
What is acute?
If one leg of a 45-45-90 triangle is x, these are the lengths of the other two sides.
What is:
Other leg: x
Hypotenuse: x√2?
Simplify √24
What is 2√6?
What is a right triangle?
Find the midpoint between (0,0) and (6,10)
What is (3,5)?
This type of triangle has 2 congruent sides.
What is isosceles?
If the shorter leg of a 30-60-90 triangle is x, these are the lengths of the other two sides.
What is:
Longer leg: x√3
Hypotenuse: 2x?
Simplify √120
What is 2√30
What is 5?
Find the distance between the points (3,11) and (-1,10).
What is √17?
DAILY DOUBLE
The sides of a triangle are 3.1, 4.7, and 5.5. Classify the triangle as acute, right, or obtuse.
What is acute?
A 45-45-90 triangle has a leg with length 8. This is the length of the hypotenuse.
What is 8√2?
Rationalize the denominator of 6/√3 and fully simplify the resulting fraction.
What is 2√3?
If the two legs of a right triangle are 12 and 15, this is the length of the hypotenuse (Must correctly simplify for credit).
What is 3√41?
Find the midpoint of the segment created between the points (2,15) and (11, 27).
What is (6.5, 21)?
a=4, b=6, and c=7. Classify the triangle as acute, obtuse, or right. Then, Classify the triangle as isosceles, equilateral, or scalene.
What is acute and scalene?
The hypotenuse of a 45-45-90 triangle has length 12. This is the length of each leg.
What is 6√2
Rationalize the denominator of (2√5)/√8 and fully simplify the resulting fraction.
What is (√10)/2?
If one leg of a right triangle is 7 and the hypotenuse of the triangle is √97, find the other leg of the triangle. Answer must be simplified to earn credit.
What is 4√3
Find the distance between the points (-27,41) and (11,-50). If you simplify you will get double points
What is √9725 = 5√389
Point A(0,0)
Point B(2,0)
Point C(1,√3)
Find the length of each leg of the triangle, then classify it based on its angles and side lengths.
What is an acute, equilateral triangle.
The longer leg of a 30-60-90 triangle is 15. This is the length of the hypotenuse.
Hint: Find the short leg first.
What is 10√3?