Find a rational approximation, to the nearest tenth, for the radical expression. $2 \sqrt { 19 } - 5 \sqrt { 19 } + 8 \sqrt { 19 } - 3 \sqrt { 19 } - 9 \sqrt { 19 }$
A) -26.3
B) -29.2
C) -30.7
D) -28.8
E) -30.5

Question

Quizplus · Accepted Answer

First, combine like terms: $2\sqrt{19} - 5\sqrt{19} + 8\sqrt{19} - 3\sqrt{19} - 9\sqrt{19} = (2 - 5 + 8 - 3 - 9)\sqrt{19} = -7\sqrt{19}$. The decimal approximation of $\sqrt{19}$ is about 4.3589. Multiplying this by -7 gives approximately -30.5123, which rounds to -30.5.

Find a Rational Approximation, to the Nearest Tenth, for the Radical