Question

Use Property 1 for radicals to simplify the following radical expression as much as possible. Assume the variable represents a positive number.

Answer 1

\[2a \sqrt[3]{8a^4}\]

Answer 2

factor 8

Answer 3

4,2

Answer 4

factor it further

Answer 5

2,2

Answer 6

so
8 = 2*2*2 = 2^3
right ?
\(x^4 = x \times x \times x \times x = x^3 \times x\)
got this ?

Answer 7

I think so...

Answer 8

Oh, yea i got it

Answer 9

i am paring 3 constants and variables this time (instead of 2 which i did last time) because in this case, its cube root, instead of square root

Answer 10

ok, I'm ready

Answer 11

\(\large \sqrt[3]{\heartsuit ^3}= \heartsuit\)

Answer 12

\(\large \sqrt[3]{\heartsuit ^3}= (\heartsuit)^{3/3}= \heartsuit \)

Answer 13

2

Answer 14

\(\Large 2a \sqrt[3]{8a^4} = 2a \sqrt[3]{8} \sqrt[3]{a}\sqrt [3]{a^3}=..\)

Answer 15

\(\Large 2a \sqrt[3]{8a^4} = 2a \sqrt[3]{2^3} \sqrt[3]{a}\sqrt [3]{a^3}=..\)

Answer 16

I know the 3s cancel out

Answer 17

so
\(\Large 2a \sqrt[3]{8a^4} = 2a \times 2 \times \sqrt[3]{a}\times a=..\)
got this ?

Answer 18

yup

Answer 19

simplify

Answer 20

4a?

Answer 21

2a times 2a = 4a^2
\(\Large 4a^2 \times \sqrt[3]a\)
thats it!

Answer 22

Ohhhhhh! Thanks

Answer 23

welcome ^_^