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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.

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))#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.