Question

How would i simplify these radicals?

Answer 1

\[\sqrt[3]{16} + \sqrt[3]{54}\]

Answer 2

\[2(\sqrt[3]{40}) - \sqrt[3]{5}\]

Answer 3

\[5(\sqrt[3]{48}) - 2(\sqrt[3]{162})\]

Answer 4

by factoring the numbers under the radicals

Answer 5

what are the indeces? 2? sorry..kinda hard to read...

Answer 6

at least that is a good first step

Answer 7

they are 3's

Answer 8

you can right-click to make it larger

Answer 9

so nicole, what is the prime factorization of 16 ?

Answer 10

2,2,2,2 ?
so \[2^{4}\]

Answer 11

right
now we want the cubed root of that
so we want to break this up so we can recognize the powers of 3
so note that this is\[\sqrt[3]{2^3\cdot2}=2\sqrt[3]2\]make sense?

Answer 12

\[\sqrt[3]{16}=\sqrt[3]{2^4}=\sqrt[3]{2^3\cdot2}=\sqrt[3]{2^3}\cdot\sqrt[3]2=2\sqrt[3]2\]

Answer 13

how does \[\sqrt[3]{2^{3}\times 2} = \sqrt[3]{2^{3}}\] ? :S

Answer 14

it doesn't, read above more closely

Answer 15

\[\sqrt[3]{2^{3}\cdot 2} = \sqrt[3]{2^{3}}\cdot\sqrt[3]2\]

Answer 16

i meant \[\sqrt[3]{2^{3}} \times \sqrt[3]{2}\]

Answer 17

because powers (and therefor roots) are distributive over multiplication
test it...

Answer 18

\[\sqrt{36}=\sqrt{4\cdot9}=\sqrt4\cdot\sqrt9=2\cdot3=6\]it's just true :)

Answer 19

oh okay, now i get it :)
yeah that does make sense

Answer 20

so you now see how\[\sqrt[3]{16}=2\sqrt[3]2\]?
if so try the next one\[\sqrt[3]{54}\]

Answer 21

\[\sqrt[3]{54} = \sqrt[3]{2 \times 3^{3}} = \sqrt[3]{2} \times \sqrt[3]{3} \] ? :S

Answer 22

\[= 3\sqrt[3]{2} \]

Answer 23

yes, nice :)
now what is the final answer?

Answer 24

the final answer is \[5\sqrt[3]{2}\]

Answer 25

exactly :)
good job

Answer 26

thanks ! :) i'll get back to yo on the other questions once i finish them.

Answer 27

You're welcome :)

Answer 28

\[2(\sqrt[3]{40}) - \sqrt[3]{5} \]\[= 2(\sqrt[3]{2^{3}\times 5}) - \sqrt[3]{5} \]\[= 2(2\sqrt[3]{5}) - \sqrt[3]{5} \]\[= 4\sqrt[3]{5} - \sqrt[3]{5} \]\[= 3\sqrt[3]{5} \]

\[5(\sqrt[3]{48}) - 2(\sqrt[3]{162}) \]\[= 5(\sqrt[3]{2^{4} \times 3}) - 2(\sqrt[3]{3^{4} \times 2}) \]\[= 5(\sqrt[3]{2^{4}} \times \sqrt[3]{3}) - 2(\sqrt[3]{3^{4}} \times \sqrt[3]{2}) \]\[= 5(2\sqrt[3]{2} \times \sqrt[3]{3}) - 2(3\sqrt[3]{3} \times \sqrt[3]{2}) \]\[= 5(2\sqrt[3]{6}) - 2(3\sqrt[3]{6}) \]\[= 10\sqrt[3]{6} - 6\sqrt[3]{6} \]\[= 4\sqrt[3]{6}\]

Answer 29

wow that took a while for me to get on here. lol

Answer 30

did i take the right steps? :)

Answer 31

that looks perfect :D
excellent job :)