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

Question

666 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-31T22:35:23

See a solution process below:

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.