Why can you not add #2sqrt2# and #4sqrt3# together?

2 Answers
Meave60
Apr 22, 2015

In order to add square roots and keep them in square root form, they must have the same radicand (number under the radical). Since #2sqrt2# and #4sqrt3# have different radicands they cannot be added without the use of a calculator, which would give you a decimal number. So the answer to #2sqrt2+4sqrt3# is #2sqrt2+4sqrt3# if you want to keep it in square root form. Its like trying to add #2x+4y#. Without actual values for #x# and #y#, the answer would be #2x+4y#.

If you use a calculator, #2sqrt2+4sqrt3=9.756630355022#

Jim H
Apr 22, 2015

You can add the numbers. But any attempt to write the sum as single whole number times a single root of a whole number will not work.

You could write the sum as
#2(sqrt2 + 2sqrt3)# but it's not clear that that is simpler.

You could 'irrationalize' denominators and write:
#4/sqrt2 + 12/sqrt3# but that is the opposite of simpler.

You could continue by getting a common denominator.

#(4sqrt3+12sqrt2)/sqrt6#

But none of these are simpler in any clear way.

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