Subject: simplifing radicals
Name: Christin
Who are you: Student

i would like for you to solve this problem??
6 square root 8

 

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 32 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 (32 x 2)1/2. But when you raise a product to an exponent, you are really just raising each factor to that exponent, so

(32 x 2)1/2 = (32)1/2 x 21/2

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

(32)1/2 = 32 x 1/2 = 31 = 3.

And anything raised to the one-half is the square root of that thing, so:
21/2 = √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.