Complete the statement. $5 \sqrt { 98 } + 10 y \sqrt { 162 } = 5 \sqrt { 2 } ( \quad ? )$
A) $7 + 9 y$
B) $14 + 81 y$
C) $7 + 18 y$
D) $9 + 14 y$
E) $9 + 7 y$

Question

Quizplus · Accepted Answer

First, simplify the square roots:
$5\sqrt{98} = 5\sqrt{2\cdot49} = 5\cdot7\sqrt{2} = 35\sqrt{2}$
$10y\sqrt{162} = 10y\sqrt{2\cdot81} = 10y\cdot9\sqrt{2} = 90y\sqrt{2}$
Now substitute back into the original equation:
$35\sqrt{2} + 90y\sqrt{2} = 5\sqrt{2}(7 + 18y)$
Therefore, the answer is (C) $7 + 18y$.

Complete the Statement 598+10y162=52(?)5 \sqrt { 98 } + 10 y \sqrt { 162 } = 5 \sqrt { 2 } ( \quad ? )598​+10y162​=52​(?)

Complete the Statement $5 \sqrt { 98 } + 10 y \sqrt { 162 } = 5 \sqrt { 2 } ( \quad ? )$