Question

What is the following quotient? StartFraction StartRoot 6 EndRoot + StartRoot 11 EndRoot Over StartRoot 5 EndRoot + StartRoot 3 EndRoot EndFraction StartFraction StartRoot 30 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot + StartRoot 33 EndRoot Over 8 EndFraction StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2 EndFraction Seventeen-eighths Negative five-halves

Answer 1

Answer: B. square root 30- 3 root 2 plus square root 55- square root 33/ 2

Explanation:

its right

Answer 2

StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2

Explanation:

Given the surdic equation as shown
`(√(6)+√(11) )/(√(5)+√(3) )\\`

To find the quotient, we will rationalize by multipying both numerator and denominator of the function by the conjugate of the denominator.

Given the denominator
`√(5)+√(3)`, its conjugate will be
`√(5)-√(3)`

Multiplying through by
`√(5)-√(3)`, we have;

`= (√(6)+√(11) )/(√(5)+√(3) ) * (√(5)-√(3) )/(√(5)-√(3) )\\`

`= (√(30)- √(18)+√(55)-√(33))/(2)\\= (√(30)- √(9*2)+√(55)-√(33))/(2)\\= (√(30)- 3√(2)+√(55)-√(33))/(2)`

The final expression gives the requires answer