help solving

Question

 

                        __

                     √18__

                        __

                      √8  - 3

 

 

 

would you help me simplify and solve this equation

 

 

 

Answer 1

multiply the top and bottom of the fraction by √8 +3 (this is called the denominator's conjugate):

   √18       (√8 +3)     √18 x (√8 + 3)

   ——    x  ————  =  ————————    

(√8 - 3)    (√8 +3)     (√8 - 3) x (√8 + 3)

 

from there FOIL the bottom and distribute the top:

 

   top: 

√18 x (√8 + 3) = √18 x √8 + √18 x 3 = √(18 x 8) + 3√18 = √144 + 3√(9 x 2) = √(12²) + 3√(3² x 2) = 12 +3 x 3 x √2 = 12 +9√2.

 

   bottom:

(√8 - 3) x (√8 + 3) = √8 x √8 + √8 x 3 + -3 x √8 + -3 x 3 = √(8 x 8) + 3√8 - 3√8 -9 = 8 - 9 = -1.

 

FOIL: First, Outer, Inner, Last (as shown above)

 

so at last we have:  

12 + 9√2

—————  = -12 - 9√2.

   - 1

Answer 2

you could begin by simplifying sqrt(18) and sqrt(8) but that is not imperative

simplify sqrt(18)/[sqrt(8)-3]

multiply both terms by sqrt(8)+3

sqrt(18)[sqrt(8)+3]/[sqrt(8)-3][sqrt(8)+3]

sqrt(18*8)+3sqrt(18)/8-9

sqrt(144)+3sqrt(18)/(-1)

12+3sqrt(2)sqrt(9)/(-1)

12+3*3*sqrt(2)/(-1)

12+9sqrt(2)/(-1)

-12-9sqrt(2)