Question

5√12×3√18×5√30 ?

Answer 1

See a solution process below:

Explanation:

We can rewrite this expression as:

`5 xx 3 xx 5 xx sqrt(12) xx sqrt(18) xx sqrt(30) =>`

`15 xx 5 xx sqrt(12) xx sqrt(18) xx sqrt(30) =>`

`75 xx sqrt(12) xx sqrt(18) xx sqrt(30)`

We can now use this rule for radicals to multiply the radicals:

`sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))`

`75 xx sqrt(color(red)(12)) xx sqrt(color(blue)(18)) xx sqrt(color(green)(30)) =>`

`75 xx sqrt(color(red)(12) xx color(blue)(18) xx color(green)(30)) =>`

`75 xx sqrt(216 xx color(green)(30)) =>`

`75 xx sqrt(6480)`

We can rewrite this expression as:

`75 xx sqrt(16 xx 81 xx 5)`

Now, we can use the reverse of the rule above to simplify the radical:

`75 xx sqrt(color(red)(16) xx color(blue)(81) xx color(green)(5)) =>`

`75 xx sqrt(color(red)(16)) xx sqrt(color(blue)(81)) xx sqrt(color(green)(5)) =>`

`75 xx 4 xx 9 xx sqrt(5) =>`

`300 xx 9 xx sqrt(5) =>`

`2700 xx sqrt(5) =>`

`2700sqrt(5)`