Rationalize the denominator.
-$\frac { 9 - 10 \sqrt { 2 } } { \sqrt { 2 } + 1 }$
A) $\frac { 19 \sqrt { 2 } - 29 } { 3 }$
B) $19 \sqrt { 2 } - 29$
C) $9 - 11 \sqrt { 2 }$
D) $\frac { 9 \sqrt { 2 } - 20 } { 3 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 9 - 10 \sqrt { 2 } } { \sqrt { 2 } + 1 }$, we multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt { 2 } - 1$. This gives:$$\frac { 9 - 10 \sqrt { 2 } } { \sqrt { 2 } + 1 } \times \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } - 1 } = \frac { (9 - 10 \sqrt { 2 })(\sqrt { 2 } - 1) } { (\sqrt { 2 } + 1)(\sqrt { 2 } - 1) }$$Expanding the numerator:$$= \frac { 9\sqrt { 2 } - 9 - 20 + 10\sqrt { 2 } } { 2 - 1 }$$$$= \frac { 19\sqrt { 2 } - 29 } { 1 }$$$$= 19\sqrt { 2 } - 29$$So, the correct answer is B) $19 \sqrt { 2 } - 29$.

Rationalize the Denominator 9−1022+1\frac { 9 - 10 \sqrt { 2 } } { \sqrt { 2 } + 1 }2​+19−102​​

Rationalize the Denominator $\frac { 9 - 10 \sqrt { 2 } } { \sqrt { 2 } + 1 }$