Question

what is the simplified form of the following expression? Assume x is greater than or equal to 0 and y is greater than or equal to 0. 2(4sq root16x)-2(4sq root 2y)+34 sq root 81x)-4(4sq root32y)

Answer 1

Answer:

$338\sqrt{x} -72\sqrt{2y}$

Step-by-step explanation:

The expression is

$2(4\sqrt{16x})-2(4\sqrt{2y}+34 \sqrt{81x}-4(4\sqrt{32y} )$

Where $x\geq 0$ and $y\geq 0$

First, we use distributive property

$8\sqrt{16x}-8\sqrt{2y}+34\sqrt{81x}-16\sqrt{32y}$

Then, we simplify square roots

$8(4)\sqrt{x} -8\sqrt{2y}+34(9)\sqrt{x} -16(4)\sqrt{2y}$

Now, we multiply and group similar roots

$32\sqrt{x} -8\sqrt{2y} +306\sqrt{x} -64\sqrt{2y} \\(32+306)\sqrt{x} +(-8-64\sqrt{2y} )\\338\sqrt{x} -72\sqrt{2y}$

Therefore, the simpliest form of the given expression is

$338\sqrt{x} -72\sqrt{2y}$

Answer 2

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