Question

Multiply. √6x⋅√15xy⋅√20 Please answer as quickly as possible

Answer 1

`\boxed{30√(2) x^2 y}`

Explanation:

`√(6) *x*√(15) * x*y*√(20)`

`\sf Multiply`

`√(6)√(15)√(20)*x*x*y`

`√(6*15*20)*x^2 *y`

`√(1800)x^2y`

`\sf Simplify`

`√(900) √(2) x^2y`

`30√(2) x^2 y`

Answer 2

`30x√(2y)`

Explanation:

First, multiply sqrt.(6x) by sqrt.(15xy)

That equals sqrt.
`\sqrt{90x^(2)y } *√(20)`

then, rewrite
`90x^(2) y` as (3x)^2 * (10y)

you have
`\sqrt{(3x)^(2) *(10y)} *√(20)`

Next, pull the terms from out under the radical, to get:

`3x√(10y) *√(20)`

Now rewrite 20 as 2^2 * 5

You get
`3x√(10y) *(2√(5) )`

Multiply everything together to get:
`6x√(50y)`

Now rewrite 50 y as 5^2 * 2y

You end up with
`6x\sqrt{5^(2)*(2y)}`

Then, pull out the terms from under the radical. You get:

`6x(5√(2y))`

Finally, multiply the 5 and 6 together to get:
`30x√(2y)`