19.3k views
0 votes
1. Write the expression in simplified radical form. Show your work. 3 – 2√11/ 2 +√11

User Smurker
by
8.5k points

2 Answers

5 votes
write it down again
you mean (3-2√11)/(2+√11) I guess
(3-2√11)(2-√11)/(2+√11)(2-√11)
(28-7√11)/(-7)
therefore the answer is √11-4

User Vaclav
by
9.0k points
3 votes
ANSWER


√(11) - 4


Step-by-step explanation

The given radical expression is


(3 - 2 √(11) )/(2 + √(11) )

We rationalize the radical expression by multiplying both the numerator and denominator by the conjugate of

2 + √(11)

which is


2 - √(11)

This will give us,


(3 - 2 √(11) )/(2 + √(11) ) * (2 - √(11) )/(2 - √(11) )



((3 - 2 √(11))(2 - √(11) ) )/((2 + √(11))(2 - √(11) ) )
We expand the numerator and also apply difference of two squares to the denominator.



\frac{6 - 3 √(11) - 4 √(11) + 2(11)}{ {2}^(2) - { (√(11) )}^(2) }

This simplifies to,



(6- 3√(11) - 4 √(11) + 22)/( 4- 11)



(28- 7 √(11) )/( - 7)


We now share the denominator for the numerators to obtain,



- (28)/(7) + (7 √(11) )/(7)

This finally gives,


- 4 + √(11) = √(11) - 4