How do you simplify #(1+ 2 sqrt(3)) /( 1+ sqrt(3))#?

Answer 1

Isaiah Anthony

#=(5-sqrt3)/2#

#=(2sqrt3+1)/(sqrt3+1)=(2sqrt3+1)/(sqrt3+1)xx(sqrt3-1)/(sqrt3-1)# #=(2sqrt3*sqrt3+sqrt3-2sqrt3-1)/(3-1)# #=(5-sqrt3)/2#

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Answer 2

Hazel Anglin

To simplify the expression (1+ 2 sqrt(3)) /( 1+ sqrt(3)), we can use the conjugate of the denominator to eliminate the square root.

The conjugate of 1+ sqrt(3) is 1- sqrt(3).

To simplify, we multiply both the numerator and denominator by the conjugate:

[(1+ 2 sqrt(3)) /( 1+ sqrt(3))] * [(1- sqrt(3))/(1- sqrt(3))]

Expanding this expression gives us:

[(1+ 2 sqrt(3))(1- sqrt(3))] / [(1+ sqrt(3))(1- sqrt(3))]

Simplifying further:

(1 - sqrt(3) + 2 sqrt(3) - 2 sqrt(9)) / (1 - sqrt(3) + sqrt(3) - sqrt(9))

Combining like terms:

(-1 + sqrt(3)) / (-1 + sqrt(3))

Since the numerator and denominator are the same, they cancel out, leaving us with:

Therefore, the simplified form of (1+ 2 sqrt(3)) /( 1+ sqrt(3)) is 1.

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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.