unit 1) topic 1 - radicals

Question 1

whats the rule with restrictions when its a cube root

Answer 1

it always has no restriction

Question 2

whats the rule when you have a even index and a even exponent on your variable and multiplying

Answer 2

it’ll have no restriction because it stops all chances of a negative base

Question 3

whats the rule when theres a even index and a addition sign or a subtraction sign

Answer 3

you would write a ≥ 0 towards the radicand then you would solve as if the sign is an equal one and isolate variable then write (variable )ER

Question 4

when would you have to flip the ≥ sign

Answer 4

when multiplying or dividing with by a negative

Question 5

whats the rule when even and multiplying by odd exponent

Answer 5

it’ll be (variable ) ≥ 0
then (variable)ER

Question 6

whats not able to happen on the denominator

Answer 6

it can never =0

Question 7

What do you do to the exponents in radical when simplifying

Answer 7

You turn them into groups depending on the index the full groups go on out side half groups on inside

Question 8

whats the last step you have to do you do when dividing a radical

Answer 8

check to see if you can simplify radicand as normal if pc or ps

Question 9

when adding / subbing radicals what can you combine and not combine

Answer 9

you can only combine things with the same index and the same radicand

Question 10

whats the first step when adding / subtracting

Answer 10

is to simplify then add sub like radicals if there are none just write beside the radicals you can

Question 11

what happens when theres a ps or pc in the radicand

Answer 11

it moves outside the radicand and then if theres a coeff they would be timesed by eachother

Question 12

how do you multiply radicals

Answer 12

you times radicands by eachother and coeffs by eachother oly when same index

Question 13

what do you need to rememeber to do to the exponents in multiplication

Answer 13

you need to rememebr to add them then put them in groups according to the index

Question 14

what does conjugate mean

Answer 14

it stands for the same equation just has - and the other is +

Question 15

what are the products of conjugate radicals always

Answer 15

they always end up rational because the radicals with one + and one - always cancel out

Question 16

what can you NOT have when dividing radicals

Answer 16

• you can never have radicals that are decimals
• in the denominator
• and can never = 0

Question 17

when writing restictions for dividing radicals and theres a radical on the denom with variables and on top whats sign

Answer 17

it would have to work for top and bottem so it cant be ≥ and would have to be >

Question 18

what steps do you take when dividing decimials

Answer 18

• you divide coeff and radicands then sub any varibles
• then make sure fully simplifyed and there can be no pc or ps taken out

Question 19

what method do you have to use when you cannot divide radicals without getting dec

Answer 19

you have to do the single term denominator

Question 20

what does the single term denominator involve

Answer 20

• you times the top and the bottem by whatevers on the denominator
• then you simplify to ensure no ps pc
• then divide top by bottem

Question 21

what does degree 2 equations stand for

Answer 21

you have two things on both sides of the equation so thats when you have 2 possible answers

Question 22

what steps include a degree 2 equation

Answer 22

1- state restiction
2- isolate radicand
3-square both sides to eliminate root
4-foil side without square root
5- add liketerms then move things to positive side of equation
6- factor then write out product and sum of equation = to 0
7- verify equation

Question 23

steps to a degree one equation

Answer 23

state restriction
isolate radicand
square both sides
solve for varible
verify

Question 24

when degree 2 how do you find restriction if both equations in root

Answer 24

solve then pick the number thats smaller so itll work for both equation varibles