Question

Simplify: 5sqrt27 3sqrt9
A. 3^1/3
B. 3^4/5
C. 3
D. 3^6/75
E. none of these

Answer 1

\[\sqrt[5]{27\sqrt[3]{9}}\]

Answer 2

@bibby

Answer 3

what I'd do is write 27 and 9 as powers of 3

Answer 4

so set it up like \[27^{3}*9^{3}\] ?

Answer 5

no as powers of 3
so \(27 = 3^3\)
\(9 = 3^2\)

Answer 6

okay so what would i do with them?

Answer 7

plug them into the sqrt instead?

Answer 8

\(\huge \sqrt[5]{27\sqrt[3]{9}}=\sqrt[5]{3^3\sqrt[3]{3^2}}\)

you can then use properties of exponents to simplify

Answer 9

okay im not sure how to do that. can you walk me through it?

Answer 10

yeah.

\(\huge \sqrt[a]{b}=b^{\frac{1}{a}}\) so:
\(\large \sqrt[3]{3^2}=3^{\frac{2}{3}}\)

Answer 11

apply that to the root: \(\huge \sqrt[5]{3^3\sqrt[3]{3^2}}=\sqrt[5]{3^33^{\frac{2}{3}}}\)

Answer 12

recall that \(a^m*a^n=a^{m+n}\)

Answer 13

so \(\huge 3^3*3^{\frac{2}{3}}=3^{3\frac{2}{3}}\)

Answer 14

we rewrite it as an i mproper fraction and do one last simplification
brb piss

Answer 15

so what we have now is \(\huge \sqrt[5]{3^{\frac{11}{3}}}\)

Answer 16

okay.

Answer 17

use the properties of roots then

Answer 18

i'm getting none of the answer choices...so E?

Answer 19

yep

Answer 20

alright, thank you :)