Question

What is the following quotient?

9+ √2 / 4- √7
a. 9√7+√14 / -3
b. 36-9√7+4√2-√14 / 9
c. 36+9√7+4√2+√14/9
d. 79/9

Answer 1

C)

Explanation:

Rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.

Conjugate of 4 - √7 = 4 + √7

`\sf (9 +√(2))/(4-√(7))= ((9+√(2))(4+√(7)))/((4-√(7))(4+√(7)))`

`\sf \bf Use \ FOIL \ method\\\\=(9*4 + 9*√(7)+√(2)*4+√(2)*√(7))/(4^2 -(√(7))^2)`

`\sf = (36+9√(7)+4√(2)+√(14))/(16-7)\\\\\\=(36+9√(7)+4√(2)+√(14))/(9)`