How do you simplify #9/(6-sqrt8)#?

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Answer 1 · 2017-07-19T04:59:25

Multiply the top and bottom by #(6 + sqrt8)# to make a difference of two squares and remove the square root.

The difference of two squares:
#(a + b)(a -b) = a^2 - ab + ab -b^2 = a^2 - b^2#

# = (9(6+sqrt8))/((6-sqrt8)(6+sqrt8))#

# =(54+9sqrt8)/(6^2 - (sqrt8)^2)#

# =(54+9sqrt8)/(36-8)#

#=(54+9sqrt8)/28#

This is now simplified, as a fraction can have a root on top, but not on the bottom (as then it is irrational).

You could also round this value to 2.84, but the answer calculated is exact.