Unit 10 - Radicals & Right Triangles

Question 1

What is a rational number?

Answer 1

Number that can be written as a fraction

Question 2

What is an irrational number?

Answer 2

Number that cannot be written as a fraction

Question 3

How do you simplify variables with exponents in radicals? (2)

Answer 3

1. If exponent is even, divide exponent by 2
2. If exponent is odd, drop exponent by 1 and simplify

Question 4

What is needed when adding and subtracting?

Answer 4

Radicals must have common radicands to be added or subtracted

Question 5

How do you multiply and divide radicals?

Answer 5

Multiply/divide the insides and multiply/divide the outsides

Question 6

Why do we rationalize the denominator? (2)

Answer 6

1. A fraction isn’t simplified if there’s a radical in denominator
2. Find an equivalent of fraction w/ a rational denominator

Question 7

How do you rationalize a monomial denominator? (2)

Answer 7

Multiply the numerator & denominator by the radical of the denominator

Question 8

What a tip in rationalizing to keep in mind?

Answer 8

RATIONALIZING SHOULD BE YOUR LAST STEP

Question 9

How do you rationalize a binomial denominator?

Answer 9

Multiply the numerator & denominator by the conjugate of the denominator

Question 10

What is a conjugate of an expression?

Answer 10

The exact same expression, but you are just changing the sign

Question 11

How do you find the multiplicative inverse? (2)

Answer 11

1. Find the reciprocal of the number
2. If there is a radical in the denominator, rationalize it

Question 12

What is the 45 - 45 - 90 Triangle Theorem? (2)

Answer 12

1. Legs are congruent
2. Hypotenuse is √2 times the leg

Question 13

What is the 30 - 60 - 90 Triangle Theorem? (3)

Answer 13

1. Opposite 30 Degree Angle - L (Small)
2. Opposite 60 Degree Angle - L√3 (Medium)
3. Opposite 90 Degree Angle - 2L (Big)

Question 14

What is the area and perimeter of a rectangle?

Answer 14

A: lw
P: 2l + 2w

Question 15

What is the area and perimeter of a square?

Answer 15

A: S²
P: 4s

Question 16

What is the area and perimeter of a triangle?

Answer 16

A: 1/2bh
P: s1+s2+s3

Question 17

What is the area and circumference of a circle?

Answer 17

A: 𝜋𝑟2
C: 2r𝜋

Question 18

What is the area and perimeter of a parallelogram?

Answer 18

A: bh
P: 2 (b+s)

Question 19

What is the area and perimeter of a trapezoid?

Answer 19

A: ½ (b1 + b2) h
P: 𝑏1+𝑏2+𝑠1+𝑠2

Question 20

What do they mean when they say put your answer as an “exact answer”

Answer 20

1. Irrational numbers shouldn’t be rounded
2. Answer should contain radicals, fractions & in terms of pi