unit 3

Question 1

simplifying radicals

Answer 1

find biggest perfect square, simplify to its entirety

Question 2

simplyifying radicals with variables

Answer 2

divide exponent on inside by the root index

Question 3

rationalize the denominator of square root expressions

Answer 3

multiply top and bottom by that sqaure root
- if there is more than 1 term, multiply it by its conjugate (FL for bottom)

Question 4

adding/subtracting radical expressions

Answer 4

• radicand needs to be the same. simplify each expression to have the same radicand, then combine like terms

Question 5

multiplying radical expressions

Answer 5

radicands don’t have to be the same, MULTIPLE WAYS based on the expression
1) multiply outside/outside and inside/inside
2) distribute and combine like terms
3) foil, combine like terms, simplify radicals if necessary
4) sqaure and rewrite as a foil problem

Question 6

solving radical equations

Answer 6

• isolate the radical
• sqaure both sides
• check solutions with original question!!!!!! this is because there may be extraneous solutions
• move everything to one side (quadratic) or get variable alone (solve for x) (linear) and solve
• for cube/4th root do the same except raise to the 3rd/4th power

Question 7

solving double radical equations

Answer 7

• isolare one of the radicals
• square both sides but foil one side
• isolate remaining radical as much as possible
• sqaure both sides
• check solutions

Question 8

imaginary numbers

Answer 8

sqaure root of negative 1 = i
- if you simplify a radical with even root index and negative radicand, get rid of i

Question 9

complex numbers

Answer 9

• imaginary (i) vs real numbers)
• complex # form: a + bi

Question 10

a

adding/subtracting complex numbers

Answer 10

• combine real exponents with each other and imaginary components with each other
• sum= resultant
• follows a + bi

Question 11

multiplying complex numbers

Answer 11

• each must be written as a + bi
• foil/multiply as is

Question 12

dividing complex numbers

Answer 12

• needs to be written in a + bi form
• multiply top and bottom by conjugate of denominator, foil both top and bottom and then combine like terms
• i cannot be in the denominator

Question 13

factoring the sum of perfect sqaures

Answer 13

• MUST use i form
• (a + bi) (a-bi) = a2 + b2
• ex. x2 - 81
• (x+9i) (x-9i)

Question 14

powers of i

Answer 14

0 = i0= 1
0.25= i1= i
0.5= i2= -1
0.75= i3= -i
always pattern of (1,i, -1, -j_
i by itself = 0
ex. i4= 1. i5= i, i6= -1, i7= -i
- to simplify power of i, divide by 4 to solve