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How do you simplify #sqrt2(5+sqrt8)#?

Answer 1

Kennedy Adams

#sqrt(2)(5+sqrt(8))=color(green)(5sqrt(2)+4)#

#sqrt(2)(5+sqrt(8))# #color(white)("XXX")=sqrt(2) * 5 + sqrt(2) * sqrt(8)# (distributive property)

#color(white)("XXX")=5sqrt(2)+sqrt(16)#

#color(white)("XXX")=5sqrt(2)+4#

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Answer 2

Kennedy Adams

To simplify sqrt2(5+sqrt8), we can first simplify the square root of 8. The square root of 8 can be written as the square root of 4 times the square root of 2, which simplifies to 2 times the square root of 2.

So, sqrt8 is equal to 2sqrt2.

Now, we can substitute this value back into the original expression: sqrt2(5+sqrt8) becomes sqrt2(5+2sqrt2).

To simplify further, we can distribute the square root of 2 to both terms inside the parentheses: sqrt2(5+2sqrt2) = 5sqrt2 + 2(sqrt2)^2.

Simplifying the last term, (sqrt2)^2 is equal to 2.

Therefore, the simplified form of sqrt2(5+sqrt8) is 5sqrt2 + 4.

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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.