Hi Christian. Try factoring the quantity under the radical (in this case, that means factoring 8).
I'll show you what I mean with other numbers: Simplify 4 square root 18. Leave the 4 alone for now. Let's factor 18: it is 3 x 3 x 2. So that is 3^{2} x 2.
The next step is to write it out using exponents. Remember that the square root sign is just like an exponent one half, so √18 = (18)^{1/2}.
That means (3^{2} x 2)^{1/2}. But when you raise a product to an exponent, you are really just raising each factor to that exponent, so
(3^{2} x 2)^{1/2} = (3^{2})^{1/2} x 2^{1/2}
Now remember that when you have something raised to an exponent, and the whole thing raised to another exponent, then you can multiply the exponents, so
(3^{2})^{1/2} = 3^{2 x 1/2} = 3^{1} = 3.
And anything raised to the onehalf is the square root of that thing, so:
2^{1/2} = √2.
So we have square root of 18 = 3 x √2.
Since we started out with 4 square root 18, we multiply it by four:
4 x 3 x √2 = 12 x √2.
So it is solved now. Try it with your numbers.
Stephen La Rocque.
