Question

What is the following quotient? 1 divided by 1+ square root 3

Answer 1

The right option is D -1+√3/2

Explanation:

To find the quotient of the sure function 1/1+√3, we will rationalize the surd function by multiplying the numerator and the denominator of the surd by the conjugate of its denominator.

Given he denominator to be 1+√3, the conjugate of 1+√3 is 1-√3

Multiplying by 1-√3 will result in the following;

1/1+√3×1-√3/1-√3

= 1-√3/(1+√3)(1-√3)

= 1-√3/1-√3+√3-√9

= 1-√3/1-√9

= 1-√3/1-3

= 1-√3/-2

= -(1-√3)/2

= -1+√3/2

The right option is D -1+√3/2

Answer 2

4th option

Explanation:

The given expression is:

`(1)/(1+√(3))`

In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with
`1-√(3)`, as shown below:

`(1)/(1+√(3))\\=(1)/(1+√(3)) * (1-√(3))/(1-√(3))\\=(1-√(3))/((1)^(2)-(√(3))^(2))\\\\ =(1-√(3))/(1-3)\\\\ =(1-√(3))/(-2)\\\\ =(-1(1-√(3)))/(2)\\\\ =(-1+√(3))/(2)`

Thus, 4th option gives the correct answer.