Question

PLEASE help me. I will give a medal and fan you.

Which of the following is equal to square root of the cube root of 6?

6 1/6
6 1/3
6 2/3
6 3/2

Answer 1

Do you have any ideas how to set this up? It helps it you know exponential forms of radicals.

Answer 2

\[\sqrt{\sqrt[3]{6}}\]This is what it looks like

Answer 3

yes. sorry, i don't really know how to set it up like that.

Answer 4

The cube root of 6 in exponential form is\[6^{\frac{ 1 }{ 3 }}\]

Answer 5

\[\sqrt[3]{6}------ 6^{\frac{1}{3}}\]

Answer 6

so
\[\sqrt{6^{\frac{1}{3}}}\]
can be written as
\[6^{\frac{1}{3} \times \frac{1}{2}}\]

Answer 7

what do you get now

Answer 8

THEN you have to take that to the 1/2 power because the square root is to the 1/2 power. So this is what you have to deal with\[(6^{\frac{ 1 }{ 3 }})^{\frac{ 1 }{ 2 }}\]Do you know how to multiply exponents?

Answer 9

and could you also help me on this question?

Simplify square root of 5 multiplied by the cube root of 5

Answer 10

why dont you try that @Stormswan

Answer 11

yes, I sort of know how to.

Answer 12

The rule with this is that you multiply the exponents together. 1/2 * 1/3 = 1/6 or \[6^{\frac{ 1 }{ 6 }}\]

Answer 13

@thushananth01 i don't know how to simplify square and cubed root :((

Answer 14

could you help me?

Answer 15

square root of 5 is the same thing as\[5^{\frac{ 1 }{ 2}}\]and the cube root of 5 is the same thing as\[5^{\frac{ 1 }{ 3 }}\]When you multiply these together you follow the same rules as you would if you were multiplying \[x ^{2} \times x ^{3}\]Do you know?

Answer 16

What do you do with the exponents?

Answer 17

5 1/6?

Answer 18

You add the exponents when you multiply their bases. You have to find a common denominator between the 2 and the 3. That would be 6. So you have, when you do that,\[5^{\frac{ 3 }{ 6 }+\frac{ 2 }{ 6 }}\]What do you get when you add those exponents?

Answer 19

5 5/6 right?

Answer 20

Yep! You're right! That's 5^5/6 power. Not 5 and 5/6 like a mixed fraction. That 5/6 is an exponent. Yes? You know that, right?

Answer 21

yes. i know. thank you SO much! @IMStuck you are awesome!

Answer 22

Thank you for that; any time you need help we are all here to help you (we do math for fun in our spare time!)

Answer 23

alright! ill be sure to tag one of you next time! :)

Answer 24

We'll be here!

Answer 25

ok, thank you once again!