unit 1) topic 1 - radicals Flashcards
whats the rule with restrictions when its a cube root
it always has no restriction
whats the rule when you have a even index and a even exponent on your variable and multiplying
it’ll have no restriction because it stops all chances of a negative base
whats the rule when theres a even index and a addition sign or a subtraction sign
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
when would you have to flip the ≥ sign
when multiplying or dividing with by a negative
whats the rule when even and multiplying by odd exponent
it’ll be (variable ) ≥ 0
then (variable)ER
whats not able to happen on the denominator
it can never =0
What do you do to the exponents in radical when simplifying
You turn them into groups depending on the index the full groups go on out side half groups on inside
whats the last step you have to do you do when dividing a radical
check to see if you can simplify radicand as normal if pc or ps
when adding / subbing radicals what can you combine and not combine
you can only combine things with the same index and the same radicand
whats the first step when adding / subtracting
is to simplify then add sub like radicals if there are none just write beside the radicals you can
what happens when theres a ps or pc in the radicand
it moves outside the radicand and then if theres a coeff they would be timesed by eachother
how do you multiply radicals
you times radicands by eachother and coeffs by eachother oly when same index
what do you need to rememeber to do to the exponents in multiplication
you need to rememebr to add them then put them in groups according to the index
what does conjugate mean
it stands for the same equation just has - and the other is +
what are the products of conjugate radicals always
they always end up rational because the radicals with one + and one - always cancel out
what can you NOT have when dividing radicals
- you can never have radicals that are decimals
- in the denominator
- and can never = 0
when writing restictions for dividing radicals and theres a radical on the denom with variables and on top whats sign
it would have to work for top and bottem so it cant be ≥ and would have to be >
what steps do you take when dividing decimials
- you divide coeff and radicands then sub any varibles
- then make sure fully simplifyed and there can be no pc or ps taken out
what method do you have to use when you cannot divide radicals without getting dec
you have to do the single term denominator
what does the single term denominator involve
- 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
what does degree 2 equations stand for
you have two things on both sides of the equation so thats when you have 2 possible answers
what steps include a degree 2 equation
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
steps to a degree one equation
state restriction
isolate radicand
square both sides
solve for varible
verify
when degree 2 how do you find restriction if both equations in root
solve then pick the number thats smaller so itll work for both equation varibles
