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How do you simplify #(sqrt3 -sqrt6)/(sqrt3 +sqrt 6)#?

Answer 1

Abigail Allen

#-3+2sqrt2#

By keeping in mind the following, we can justify the denominator:

#(sqrta+sqrtb)(sqrta-sqrtb)=a-b#

Here:

#(sqrt3-sqrt6)/(sqrt3+sqrt6)#

#(sqrt3-sqrt6)/(sqrt3+sqrt6)(1)#

#(sqrt3-sqrt6)/(sqrt3+sqrt6)((sqrt3-sqrt6)/(sqrt3-sqrt6))#

#(sqrt3-sqrt6)^2/(3-6)#

#(3+6-2sqrt18)/(-3)#

#(9-6sqrt2)/(-3)=-3+2sqrt2#

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Answer 2

Kennedy Adams

To simplify the expression (sqrt3 - sqrt6)/(sqrt3 + sqrt6), we can use the conjugate of the denominator to eliminate the square roots in the numerator. The conjugate of sqrt3 + sqrt6 is sqrt3 - sqrt6.

By multiplying both the numerator and denominator by the conjugate, we get:

[(sqrt3 - sqrt6)(sqrt3 - sqrt6)] / [(sqrt3 + sqrt6)(sqrt3 - sqrt6)]

Expanding the numerator and denominator, we have:

(3 - 2sqrt18 + 6) / (3 - 6)

Simplifying further:

(9 - 2sqrt2 * 3 + 6) / (-3)

Combining like terms:

(15 - 6sqrt2) / (-3)

Finally, simplifying the expression:

-(5 - 2sqrt2)

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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.