Respuesta :
the given expression is :
2(4√16x) - 2(4√2y) + 34√81x - 4(4√32y)
⇒ 8(√16x) - 8(√2y) + 34√81x - 16√32y
⇒8×4√x - 8√2y + 34×9√x - 16√16×2y [∵ √16 = 4 and √81 = 9]
⇒32√x - 8√2y + 306√x - 16×4√2y
⇒(32√x + 306√x) - 8√2y - 16×4√2y
⇒338√x -72√2y
Answer:
[tex]338\sqrt{x} -72\sqrt{2y}[/tex]
Step-by-step explanation:
The expression is
[tex]2(4\sqrt{16x})-2(4\sqrt{2y}+34 \sqrt{81x}-4(4\sqrt{32y} )[/tex]
Where [tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]
First, we use distributive property
[tex]8\sqrt{16x}-8\sqrt{2y}+34\sqrt{81x}-16\sqrt{32y}[/tex]
Then, we simplify square roots
[tex]8(4)\sqrt{x} -8\sqrt{2y}+34(9)\sqrt{x} -16(4)\sqrt{2y}[/tex]
Now, we multiply and group similar roots
[tex]32\sqrt{x} -8\sqrt{2y} +306\sqrt{x} -64\sqrt{2y} \\(32+306)\sqrt{x} +(-8-64\sqrt{2y} )\\338\sqrt{x} -72\sqrt{2y}[/tex]
Therefore, the simpliest form of the given expression is
[tex]338\sqrt{x} -72\sqrt{2y}[/tex]
