How do you rationalize the denominator and simplify #8/(3-sqrt2)#?

Answer 1

The answer is #(24+8sqrt2)/7#.

To rationalize the denominator of a fraction, multiply both the numerator and the denominator by the denominator's conjugate.

The conjugate of #3-sqrt2# is #3+sqrt2#
#color(white)=8/(3-sqrt2)#
#=8/((3-sqrt2))color(red)(*((3+sqrt2))/((3+sqrt2)))#
#=(8(3+sqrt2))/((3-sqrt2)(3+sqrt2))#
#=(24+8sqrt2)/(3^2+color(red)cancel(color(black)(3sqrt2-3sqrt2))-(sqrt2)^2)#
#=(24+8sqrt2)/(9-2)#
#=(24+8sqrt2)/7#

This answer is as simplified as possible.

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Answer 2

To rationalize the denominator and simplify the expression 8/(3-sqrt2), we multiply both the numerator and denominator by the conjugate of the denominator, which is 3+sqrt2. This results in (8 * (3+sqrt2))/((3-sqrt2) * (3+sqrt2)). Simplifying further, we get (24 + 8sqrt2)/(9 - 2). Finally, simplifying the denominator, we have (24 + 8sqrt2)/7.

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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.

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.

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.

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.

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