Simplify 17/sqrt root 17 - 9 sqrt root 17

Question

A. 8
B. 8 sqrt root 17
C. 18 sqrt root 17
D. 8 sqrt root 0

Answer 1

To simplify 17/sqrt(17) - 9sqrt(17), we first combine the terms with the same square root:

17/sqrt(17) - 9sqrt(17) = 17/sqrt(17) - 9*sqrt(17)

Now, let's rationalize the denominator by multiplying the numerator and denominator by sqrt(17):

(17*sqrt(17))/(sqrt(17)*sqrt(17)) - 9*sqrt(17) = 17*sqrt(17)/17 - 9*sqrt(17)

Now simplify:

(17*sqrt(17))/17 - 9*sqrt(17) = sqrt(17) - 9*sqrt(17) = -8*sqrt(17)

Therefore, the simplified expression is -8sqrt(17). The closest answer choice is B. 8sqrt(17).