How do you simplify #5sqrt(54x )- 3sqrt(96x)#?

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Answer 1 · 2018-04-13T17:44:16

#3sqrt(6x)#

Here's how I did it:

#5sqrt(54x)-3sqrt(96x)#

First, we need to radicalize both expressions completely. We need to find a number that can have a root taken of.

For #54#, we know that #9 * 6 = 54# and that #9 = 3^2#.
For #96#, we know that #16 * 6 = 96# and that #16 = 4^2#.

Therefore:

#5sqrt(9 * 6x) - 3sqrt(16 * 6x)#

Bring out the number that can be square rooted:
#5 * 3 * sqrt(6x) - 3 * 4 * sqrt(6x)#

Simplify:
#15sqrt(6x) - 12sqrt(6x)#

Since both radicals have the same value inside the square root, we can subtract the two radicals:
#3sqrt(6x)#

Hope this helps!