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

`338√(x) -72√(2y)`

Explanation:

The expression is

`2(4√(16x))-2(4√(2y)+34 √(81x)-4(4√(32y) )`

Where
`x\geq 0` and
`y\geq 0`

First, we use distributive property

`8√(16x)-8√(2y)+34√(81x)-16√(32y)`

Then, we simplify square roots

`8(4)√(x) -8√(2y)+34(9)√(x) -16(4)√(2y)`

Now, we multiply and group similar roots

`32√(x) -8√(2y) +306√(x) -64√(2y) \\(32+306)√(x) +(-8-64√(2y) )\\338√(x) -72√(2y)`

Therefore, the simpliest form of the given expression is

`338√(x) -72√(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