Question

Simplify square root of 2 multiplied by the cube root of 2.

2 to the power of 1 over 6
2 to the power of 2 over 3
2 to the power of 5 over 6
2 to the power of 7 over 6

Answer 1

So your equation is:

\(\large\bf{\sqrt{2} \times \sqrt[3]{2}}\)

You would need to change these into rational exponents.

The format is:

\(\large\bf{\sqrt[n]{x^{m}}}\)

So you re-write the first one as: \(\large\bf{2^{\frac{1}{2}}}\)

and the second one as: \(\large\bf{2^{\frac{1}{3}}}\)

So we now have:

\(\large\bf{2^{\frac{1}{2}} \times 2^{\frac{1}{3}}}\)

What do we do next?

Answer 2

multiply

Answer 3

you have to multiply

Answer 4

it equals 4

Answer 5

??

Answer 6

wait

Answer 7

it equals 7 square root of 2 over 3

Answer 8

Well yes we need to multiply, `BUT` the exponents need to have the same denominator.

How would you do this?

Answer 9

ohhhh wait

Answer 10

i remember learning it but i forgot how you do it omg

Answer 11

XD okie

well to have the same denominator you need to think of a term that has a factor of 2 and 3. Which comes to mind?

Answer 12

1

Answer 13

Not quiet. How about 6?

2 x 3 = 6

so it definitely works.

Answer 14

ohhhhhhhh

Answer 15

im so stupid

Answer 16

So we multiply the fractions to get a denominator of 6.

\(\large\bf{\frac{1}{2} \times 3 = \frac{3}{6}}\)

\(\large\bf{\frac{1}{3} \times 2 = \frac{2}{6}}\)

So now you have...

\(\large\bf{2^{\frac{3}{6}} \times 2^{\frac{2}{6}}}\)

Answer 17

What is your answer?

Answer 18

the answer i got isn't an answer choice :/

Answer 19

You just need to add the exponents together, the 2 stays as 2.

\(\Large\bf{\color{red}{2^{\frac{3}{6} + \frac{2}{6}}}}\)

Answer 20

2 and 5 over 6

Answer 21

yup

Answer 22

yayyyy thank you so much! are you good with graphing stuff

Answer 23

np

kind of >.>

but i have to go sadly ;-;

Answer 24

oh okay well thank for your help!