Question

HELPPPPPPPPP i have the most trouble with math what’s the answer??

Answer 1

`√(13)-√(11)`

Explanation:

When we have an expression in this form:

`(a)/(√(x)+√(y)  )`

We need to multiply it by
`(√(x)-√(y)  )/(√(x)-√(y))`

Let's do this:

`(2)/(√(13)+√(11)  )*(√(13)-√(11))/(√(13)-√(11))\\=(2(√(13)-√(11)))/((√(13)+√(11))(√(13)-√(11)))\\=(2√(13) -2√(11) )/((√(13) )^2-(√(11) )^2)\\=(2√(13) -2√(11) )/(13-11)\\=(2√(13) -2√(11) )/(2)\\=(2(√(13) -√(11) ))/(2)\\=√(13)-√(11)`

Note: we used the property
`√(a) √(a) =a`

Answer 2

Last Option

`√(13) -√(11)`

Explanation:

To simplify the expression you must multiply the numerator and the denominator of the fraction by the conjugate of the denominator.

If you have an expression of the form

`a +b` then its conjugate will be
`a - b.`

The result of that multiplication will be

`a ^ 2 -b ^ 2`

Therefore we have the expression

`(2)/(√(13) +√(11))`

By multiplying by the conjugate of the denominator we have

`(2)/(√(13) +√(11))*(√(13) -√(11))/(√(13) -√(11))\\\\\\(2(√(13) -√(11)))/((√(13))^2 -(√(11))^2)\\\\\\(2√(13) -2√(11))/(13 -11)\\\\\\(2√(13) -2√(11))/(2)`

`=√(13) -√(11)`