Question

How do you simplify `8sqrt(200)`?

Answer 1

You check to see if you can find a perfect square to extract from the square root.

Explanation:

The only way in which you can simplify this expression is by checking to see if you can extract something from the square root.

Since `200` is not a perfect square itself, you'll have to check to see if you can write this number as a product between a perfect square and another number.

Notice that you can write

`200 = 100 * 2`

Since `100` is a perfect square, you can write

`200 = 10 * 10 * 2 = 10""^2 * 2`

This means that your original expression becomes

`8sqrt(200) = 8sqrt(10""^2 * 2) = 8 * 10sqrt(2) = color(green)(80sqrt(2))`