Can someone tutor me in multiplying and dividing radicals? Please no nonsense I want to learning

- pokemon23

Can someone tutor me in multiplying and dividing radicals? Please no nonsense I want to learning

- schrodinger

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- Mimi_x3

Hm..i said that i will help you :/

- pokemon23

|dw:1326159651743:dw|

- Mimi_x3

Just multiply.
\[5*7\sqrt{8*3} \]

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## More answers

- UnkleRhaukus

\[{1 \over√a} = {1 \over√a} \times {√a \over √a}={√a \over a}\]

- pokemon23

so?

- Mimi_x3

can't you times it.

- Mimi_x3

Yes!

- pokemon23

|dw:1326159934510:dw|

- Mimi_x3

Correct!

- Mimi_x3

Want to simplify it further?

- pokemon23

yes please

- pokemon23

how do you simplify it further?

- anonymous

what times what gives 24, 6*4
so
35(6)^(1/2)*(4)^(1/2)
or
\[35\sqrt{4}\sqrt{6}\]

- pokemon23

can we simplify it further

- anonymous

now you can take the square root of 4
which is 2
therefore you are left with
35(2)(6)^(1/2)

- anonymous

which is just equal to
\[70\sqrt{6}\]

- pokemon23

so its |dw:1326160227547:dw|

- pokemon23

how can we simplify it their?

- anonymous

you can't

- anonymous

if you take the square root of 2 you end up with an irrational number which can only be approximated

- Mimi_x3

Pokemon, you can just use a calculator to check, if you type that in the calculator, it won't equal the same to \[5\sqrt{8}*7\sqrt{3} \]

- pokemon23

|dw:1326160630061:dw| to the solution

- Mimi_x3

\[35*2\sqrt{6} \]

- Mimi_x3

since \[\sqrt{4} = 2\]

- pokemon23

how? how did you get the solution

- Mimi_x3

Hmm...where don't you understand?
It has been explained thoroughly.

- anonymous

2*2 is = 4, when you take the square of a number it will tell you what two exact numbers can be multiplied together to give you the original number

- anonymous

Radicals are simply the opposite of exponents.
If you had just say
3^(3)
=
(3)(3)(3) = 27
27^(1/3)
=3

- anonymous

Thus (4)^(1/2) = 2
because
2*2 = 4

- anonymous

You need to memorize the fundamental rule in radicals that
(ab)^(1/2) = \[\sqrt{a}\sqrt{b}\]

- anonymous

if you wish to simplify radicals further, usually I'm to lazy to do this though :d

- Mimi_x3

You can simplify it further but you don't need to, it depends on the question.

- anonymous

In your case
35(24)^(1/2) =
\[35\sqrt{6}\sqrt{4}\]

- pokemon23

thanks for the help

- anonymous

since 35 is being multiplied by the radical when (4)^(1/2) is simplified to 2 you are left with
35(2)(6)^(1/2)
if you take the square root of 6 you are going to end up with a very ugly number and in mathematics they usually like you to deal with exact numbers

- pokemon23

you can reduce to 35|dw:1326161502375:dw|

- anonymous

No problem I hope you have gained a better understanding of radicals, I would recommend look up the fundamental rules of radicals

- anonymous

Once you know all the basic algebraic laws, math becomes a lot easier

- anonymous

the final answer being 70(6)^(1/2) but I will stop posting now :D

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