Question

medal and fan

Answer 1

Most of the time, it is easier to consider radicals as fractional exponents. Then radicals are ruled by the laws of exponents.

Answer 2

im still kind of confused on the difference

Answer 3

Okay.

What can you do with

\[ \large \sqrt 3 ( \sqrt 5) \] ?

make it:

\[\large 3^{1 \over 2} (5)^{1 \over 2}\]

and just like if the exponent were a whole number:

\[\large (3 \cdot 5)^{1 \over 2} \]

Answer 4

Now for example

\[\large \sqrt 8 ( \sqrt 3) = (8\cdot 3)^{1 \over 2} = 24^{1 \over 2}\]

but if you see a factor there you want out:

\[\large 24^{1 \over 2}= (6\cdot 4)^{1 \over 2} = 4 ^{1 \over 2}\cdot 6 ^{1 \over 2}= \sqrt 4 \cdot \sqrt 6 = 2\sqrt 6 \]

Answer 5

oh ok thank you :)

Answer 6

You cannot add radicals for the same reason you cannot add numbers with exponents.

\[ \large 2^2 + 3^2 \ne (2+3)^2 \]

because two squared is four and three squared is nine, and that is not equal to five square which is twenty-five.

So
\[ \large \sqrt 2 + \sqrt 3 \ne \sqrt{2+3} \]