How do you simplify #2sqrt6+3sqrt54#?

2 Answers
Shambale
Mar 22, 2018

The answer is #11sqrt(6)#

Explanation:

Assuming you know how to simplify individual radicals, we can get more into detail about how to do this. With radicals, if they have the same base (as in the same number under the square root sign), we can simply add the coefficients together (The numbers in front of the square root sign).

However, we see that #2sqrt(6)# does not have the same base as #3sqrt(54)#.

#2sqrt(6)# cannot be simplified any further than it is, so we can assume we need to simplify #3sqrt(54)#.

To do this, we need to find perfect square factors (4, 9, 16) that can be found by breaking down the 54. What it comes out to be is 9 and 6, very nice numbers to work with:

#3sqrt(54)# = #3sqrt(6*9)#

As the 9 is a perfect square of 3, it can be brought out to the front of the equation, forming #9sqrt(6)#. Since it has the same base as #2sqrt(6)#, we can just add them together to find the answer:

#2sqrt(6)#+#9sqrt(6)#=#11sqrt(6)#

Hope this helped to clarify how to solve radicals with different bases!

Serena D.
Mar 22, 2018

#11sqrt6#

Explanation:

#2sqrt6+3sqrt54 rarr# Note that #sqrt54# can be simplified

#2sqrt6+3sqrt(9*6) rarr# 9 is a perfect square, it can be taken out of the radical

#2sqrt6+3*3sqrt(6) rarr# The square root of 9 is 3

#2sqrt6+9sqrt6 rarr# Combine the two terms

#11sqrt6#

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