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

Answer 1

#11sqrt6#

#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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Answer 2

The answer is #11sqrt(6)#

We can go into more detail about how to do this if you are familiar with simplifying individual radicals. For radicals, if they have the same base, that is, the same number under the square root sign, we can just 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)#.

Finding perfect square factors (4, 9, 16) is necessary to accomplish this. By dissecting the 54, we find that the two most manageable numbers are 9 and 6.

#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)#

I hope that this made it clearer how to deal with radicals that have different bases!

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Answer 3

To simplify 2√6 + 3√54, we can first simplify the square roots individually. The square root of 6 cannot be simplified further, but the square root of 54 can be simplified to 3√6.

So, the expression becomes 2√6 + 3√6.

Since both terms now have the same square root, we can combine them by adding their coefficients.

Therefore, the simplified form of 2√6 + 3√54 is 5√6.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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