Question

How do you evaluate `4\sqrt { 54} - 8\sqrt { 216} + 3\sqrt { 150}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite this expression as:

`3sqrt(9 * 6) - 8sqrt(36 * 6) + 3sqrt(25 * 6)`

We can then use this rule for multiplying radicals to rewrite the expression again as:

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

`3sqrt(color(red)(9) * color(blue)(6)) - 8sqrt(color(red)(36) * color(blue)(6)) + 3sqrt(color(red)(25) * color(blue)(6)) =>`

`3sqrt(color(red)(9))sqrt(color(blue)(6)) - 8sqrt(color(red)(36))sqrt(color(blue)(6)) + 3sqrt(color(red)(25))sqrt(color(blue)(6)) =>`

`(3 * 3)sqrt(color(blue)(6)) - (8 * 6)sqrt(color(blue)(6)) + (3 * 5)sqrt(color(blue)(6)) =>`

`9sqrt(color(blue)(6)) - 48sqrt(color(blue)(6)) + 15sqrt(color(blue)(6))`

Now, we can factor out the common term (`sqrt(6)`) giving:

`(9 - 48 + 15)sqrt(color(blue)(6)) =>`

`-24sqrt(color(blue)(6))`

Or

`-58.788` rounded to the nearest thousandth.