Question

write as a single radical, then simplify:
square root, of the square root of 243(x+1)

Answer 1

\[\sqrt{\sqrt{243(x+1)}}\]

Answer 2

Weird that that just posted here. Was meant to be on the last question.

Answer 3

\[\sqrt{\sqrt{243(x+1)}}\]

Answer 4

nice job!

Answer 5

thanks(:

Answer 6

\[\sqrt{\sqrt{b}}=\sqrt[4]{b}\] does that help?

Answer 7

uhm..not really. i dont know what to do. or where to start

Answer 8

what i wrote is where to start. put
\[\sqrt[4]{243(x+1)}\]

Answer 9

then you next job is to factor 243 and see if it has any fourth powers in it. if so you can pull them out

Answer 10

if you are a calculating savant you may recognize
\[243=3^5\]but my guess is you do not, so you have to factor. i would cheat

Answer 11

http://www.wolframalpha.com/input/?i=factor243
look at that! who knew?

Answer 12

i love my calculator. lol.. and okay im sorta understanding more now

Answer 13

Nice work, Satellite.

Answer 14

awesome.! haha

Answer 15

Meg, just try to get comfortable with exponent rules.

Answer 16

(Because roots are really just exponents)

Answer 17

im just learning the ones past 3... :/ dont really know them

Answer 18

i am fairly sure that your calculator will not factor, so acquaint yourself with wolfram or else do it by hand

Answer 19

ohh alright. isee.

Answer 20

Like for this one, you can rewrite it as (243(x+1)) ^ (1/2) ^(1/2)
Then you can know that with exponents, if you raise an exponent to another exponent you multiply them. So this gives:
(243(x+1))^(1/4)
And with exponents, if it's a numerator it's a power, but in the denominator it's a root. So that makes it:
\[\sqrt[4]{243(x+1)}\]

Answer 21

now you have
\[\sqrt[4]{3^5(x+1)}\] and having an exponent in the radicand larger than the index is taboo, so you think
\[3^5=3^4\times 3\] and
\[\sqrt[4]{3^4}=3\] (you do this part in your head)
giving
\[3\sqrt[4]{3(x+1)}\] as your answer

Answer 22

really mean you do that in your head. if you see
\[\sqrt[3]{x^7}\] you go right to
\[x^2\sqrt[3]{x}\]

Answer 23

here is the thinking:
"x goes in to 7 twice, with a remainder of 1"
"x^2 comes outside the radical, x^1 =x stays inside"

Answer 24

ahhh. i totally get that! thanks so much.!!

Answer 25

really? great! just to make sure though...
what is
\[\sqrt{50x^5y^3}\]?

Answer 26

(hint, the index here is 2, even though it is not written)

Answer 27

what do u mean index?

Answer 28

btw i meant
here is the thinking:
"3 goes in to 7 twice, with a remainder of 1"
"x^2 comes outside the radical, x^1 =x stays inside"

Answer 29

in the expression
\[\sqrt[4]{abc}\] 4 is the "index" and abc is the "radicand"

Answer 30

\[\sqrt[3]{x}\] reads "cubed root of x" index is 3

Answer 31

alright. my teacher is terrrible at explainng this

Answer 32

\[\sqrt{x}\] reads "square root of x" index is 2 and by convention we do not write it

Answer 33

yeah most just say "simplify" which is meaningless unless you know the specific rules for "simplest radical form"

Answer 34

if you have time read this. the rules are here

Answer 35

the answer... is it \[2\sqrt{25x^5y^3}\] ??

Answer 36

no you have a few problems here. i will talk it out.
\[50=25\times 2=5^2\times 2\] so a 5 comes out and a 2 stays in
2 (the index) goes in to 5 2 times with a remainder of 1 so x^2 comes out and x stays in
2 goes in to 3 1 time with a remainder of 1, so y^1 = y comes out and y stays in
you get
\[\sqrt{50x^5y^3}=5x^2y\sqrt{2xy}\]

Answer 37

if you want we can do another example from your homework

Answer 38

oh my gosh thanks. and okay.. ill give u one more.. hang on

Answer 39

\[\sqrt[4]{562^4}\]

Answer 40

oooh that is like asking who is buried in grants tomb

Answer 41

what is the fourth root of something raised to the power of 4?

Answer 42

\[\sqrt[4]{x^4}=?\]

Answer 43

x...

Answer 44

ohh so is the answer just 562 ?

Answer 45

yup!

Answer 46

next...

Answer 47

yay! you are really good at explaining things. im so glad you helped me. (:

Answer 48

100^-3/2 kinda simple....

Answer 49

yw. be happy to do another one if you think it would help

Answer 50

can u help with 100^3/2

Answer 51

yes. first off do you know what
\[x^{\frac{3}{2}}\] means?

Answer 52

uhmm not exactly.

Answer 53

the exponent is a fraction. it has a numerator of 3 and a denominator of 2
the numerator is the power, and the denominator is the root

Answer 54

oh okay....

Answer 55

so this means
a) cube 100, then take the square root
b) take the square root of 100, then cube

second way is easiest

Answer 56

what is the square root of 100?

Answer 57

10

Answer 58

yes. now what is
\[10^3\]?

Answer 59

1000

Answer 60

exactly
and so
\[100^{\frac{3}{2}}=\sqrt{100^3}=10^3=1000\] and you are done

Answer 61

good job

Answer 62

okay well i have some others like that but theyre just negative.. is there a difference? on how to do them that is.. like 32^-3/5

Answer 63

oh yes they are different.

Answer 64

Negative exponents move to the denominator and become positive. So 2^(-1) is the same as 1/2

Answer 65

the numerator is the power
the denominator is the root
and the minus sign means take the reciprocal

Answer 66

so just switch them around...?

Answer 67

so if you were going to compute
\[32^{-\frac{3}{5}}\] i would first compute
\[32^{\frac{3}{5}}\] and the flip the result

Answer 68

so lets go slow

Answer 69

ohh okay so same process, just flip the answer.? and oka

Answer 70

first lets compute
\[32^{\frac{3}{5}}\]

Answer 71

the numerator is 2, so second power. the denominator is 5 so 5th root. i prefer method b) from above.
what is the 5th root of 32 (make a guess, it will probably be right)

Answer 72

2 so i worked it sand got 8 as the answer...

Answer 73

and *

Answer 74

great! now we have
\[32^{\frac{3}{5}}=2^3=8\] right. so now we take care of the minus sign. take the reciprocal of 8 and you are done

Answer 75

by which i mean just flip it. answer...

Answer 76

so its... -1/8 ?

Answer 77

close but you were thinking too hard. just flip it. don't make it negative

Answer 78

oh alright. haha. (:

Answer 79

when you raise to a power if the base is positive you NEVER get a negative answer. your doing great

Answer 80

got another?

Answer 81

thank you again. (: and no im all good now that you explained it really good. i may need help again some other day. so i may ask u then but goodnight satellite..!

Answer 82

g'night