Question

How to Evaluate the following expressions



and what we call these type of expressions?

Answer 1

\[8^{1/3}\]\[\sqrt{27}/\sqrt{27}\]

Answer 2

I think I should attach the picture so you guys see much better. Please tell me how do I solve these type of expressions and what we call these expressions?

Answer 3

do you know what 4^(1/2) is?

Answer 4

No, can you please explain it?

Answer 5

its the same as sqrt(4) do you know how to do square roots?

Answer 6

No, please explain little more. What do we call these type of expressions in algebra? I have found this exercise on Wikipedia that's why I am asking. I have no idea about how to take square roots of numbers. Please if you explain it.

Answer 7

what is 2 times 2
what is 3 times 3
what is 4 times 4
tell me these things and il show you square roots

Answer 8

4
9
16

Answer 9

the square root of 4 is 2
the square root of 9 is 3
the square root of 16 is 4
you get what im saying

Answer 10

Yes, I got it. It means the opposite of square

Answer 11

so what is the cube root of 8

Answer 12

cube root of 8 is 512

Answer 13

no thats 8 cubed

Answer 14

No, it is 2 ? right

Answer 15

exactly

Answer 16

theres your first expression

Answer 17

but how do I know that I have to take the cube root or square root of the quantity while it looks like this on the Exponential power 1/4 ?

Answer 18

so the cube root of 8 is 2 becuase 2*2*2 = 8. Cube = times itself 3 times
1/4th root is times itself 4 times.
For example the square root of 16 is 4, but the 1/4th root of 16 is 2

In the same way taking 8^(2/3) is the same as taking it 8^2 and 8^(1/3) in any particulare order.

Answer 19

so you can take 16^(1/4) = 2 becuase 2*2*2*2 = 16, 32^(1/5) is 2 becuase 2*2*2*2*2 is 32

Answer 20

So, it means we have to take the root of the denominator of any expression?

Answer 21

I mean denominator of Exponential power

Answer 22

yes, if it is a fraction you take teh root, if it is a number you just take it times itself that many times, the order is unimportant, as long as you do them all

Answer 23

also sqrt(1/2) = 1/sqrt(2)

Answer 24

not all square roots turn out to be nice numbers, if they dont you usually just leave it in square root form

Answer 25

terrible drawing but you get the point

Answer 26

(1/8)^1/3 = 1/8?

Answer 27

(1/8)^(1/3) = 1/[8^(1/3)]

Answer 28

you already know 8^(1/3)

Answer 29

also anything to the negative number just means you do 1/(that number) and make it positive again
n^(-1) = 1/n
1/n^(-1) = n

Answer 30

anything to the zero = 1

Answer 31

Thanks, now how do we solve this type of expression?
\[\sqrt{27} /\sqrt[3]{9}\]

Answer 32

anything to 1 = itself

Answer 33

well there is a trick you can use, but ultimately you wont get a nice number becuase sqrt(27) is not a nice number
however you can draw out numbers from squares
for example 8^(1/2) = 4^(1/2) * 2^(1/2) = 2 * 2^(1/2)

Answer 34

what can you write sqrt(27) as to make it simpler

Answer 35

you understand how I took 4 out of 8 right?

Answer 36

3^3

Answer 37

well yea 27 is 3^3 but sqrt(27) is actually 3^(3/2)