How do you simplify #7sqrt54-sqrt24#?

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Answer 1 · 2018-04-27T12:06:12

See a solution process below:

First, we can rewrite the terms under the radicals as:

#7sqrt(9 * 6) - sqrt(4 * 6)#

Next, we can use this rule for radicals to simplify the radical terms:

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

#7sqrt(color(red)(9) * color(blue)(6)) - sqrt(color(red)(4) * color(blue)(6)) =>#

#7sqrt(color(red)(9))sqrt(color(blue)(6)) - sqrt(color(red)(4))sqrt(color(blue)(6)) =>#

#(7 * 3sqrtcolor(blue)(6)) - 2sqrt(color(blue)(6)) =>#

#21sqrtcolor(blue)(6) - 2sqrt(color(blue)(6))#

Now, we can factor out the common term:

#(21 - 2)sqrt(color(blue)(6)) =>#

#19sqrt(color(blue)(6))#