How do you simplify #sqrt(6)/(4+sqrt(2))#?

Answer 1

#(2sqrt(6)-sqrt(3))/6#

The idea is to rationalise the denominator, we can do this by multiplying the top and the bottom of the fraction by the conjugate of the bottom:

#(4-sqrt(2))/(4-sqrt(2))#

We have just took the negative of the square root term.

Now:

#sqrt6/(4+sqrt(2))*(4-sqrt(2))/(4-sqrt(2))#
#=(4sqrt(6)-sqrt2*sqrt6)/(16+4sqrt(2)-4sqrt(2)-2#
#=(4sqrt(6)-sqrt12)/14#
Transform the #sqrt(12)# term into a surd like so:
#=(4sqrt(6)-2sqrt(3))/14=(2sqrt(6)-sqrt(3))/7#
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Answer 2

To simplify the expression sqrt(6)/(4+sqrt(2)), we can multiply both the numerator and denominator by the conjugate of the denominator, which is 4-sqrt(2). This will help eliminate the square root in the denominator.

By multiplying the numerator and denominator by 4-sqrt(2), we get:

(sqrt(6)/(4+sqrt(2))) * ((4-sqrt(2))/(4-sqrt(2)))

Simplifying this expression gives us:

(sqrt(6)(4-sqrt(2))) / ((4+sqrt(2))(4-sqrt(2)))

Expanding the numerator and denominator, we have:

(4*sqrt(6) - sqrt(6)*sqrt(2)) / (16 - 2)

Further simplifying, we get:

(4*sqrt(6) - sqrt(12)) / 14

Since sqrt(12) can be simplified to 2*sqrt(3), the expression becomes:

(4sqrt(6) - 2sqrt(3)) / 14

This can be simplified further by factoring out a common factor of 2 from the numerator:

(2*(2*sqrt(6) - sqrt(3))) / 14

Finally, simplifying the expression gives us:

(2*sqrt(6) - sqrt(3)) / 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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