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How do you simplify #sqrt2 (sqrt8 + sqrt4)#?

Answer 1

Hazel Anglin

multiply and try to get rid of #sqrt()#'s if possible

#sqrt(2)(sqrt(8) + sqrt(4)) = sqrt(2)sqrt(8) + sqrt(2)sqrt(4)#

#=sqrt(16) + sqrt(2)*2 #

#= 4+2sqrt(2)# or #= 4+sqrt(8) #

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Answer 2

Abigail Allen

To simplify the expression sqrt2 (sqrt8 + sqrt4), we can first simplify the terms inside the parentheses. The square root of 8 can be simplified as sqrt(4 * 2), which equals 2 * sqrt2. The square root of 4 is simply 2.

Now, we substitute these simplified terms back into the expression: sqrt2 (2 * sqrt2 + 2).

Next, we distribute the sqrt2 to both terms inside the parentheses: 2 * sqrt2 * sqrt2 + 2 * sqrt2.

Simplifying further, we have 2 * 2 + 2 * sqrt2, which equals 4 + 2 * sqrt2.

Therefore, the simplified form of sqrt2 (sqrt8 + sqrt4) is 4 + 2 * sqrt2.

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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.